Peter Borg

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All published works

Action	Title	Year	Authors
+ PDF Chat	Solution to a $3$-path isolation problem for subcubic graphs	2024	Karl Bartolo Peter Borg Dayle Scicluna
+ PDF Chat	Upper bounds on isolation parameters	2024	Peter Borg Magdalena Lemańska Mercè Ferrater Mora Marı́a José Souto Salorio
+ PDF Chat	Isolation of squares in graphs	2024	Karl Bartolo Peter Borg Dayle Scicluna
+ PDF Chat	Proof of a conjecture on isolation of graphs dominated by a vertex	2024	Peter Borg
+ PDF Chat	Solution to a problem of Katona on counting cliques of weighted graphs	2023	Peter Borg Carl Feghali Rémi Pellerin
+ PDF Chat	Isolation of connected graphs	2023	Peter Borg
+	Isolation of regular graphs, stars and $k$-chromatic graphs	2023	Peter Borg
+	Isolation of regular graphs and $k$-chromatic graphs	2023	Peter Borg
+ PDF Chat	Isolation of Regular Graphs, Stars and $K$-Chromatic Graphs	2023	Peter Borg
+	Isolation of squares in graphs	2023	Karl Bartolo Peter Borg Dayle Scicluna
+ PDF Chat	Extensions of the Art Gallery Theorem	2022	Peter Borg Pawaton Kaemawichanurat
+ PDF Chat	The maximum sum of sizes of cross-intersecting families of subsets of a set	2022	Peter Borg Carl Feghali
+	Decreasing the maximum degree of a graph	2022	Peter Borg
+	Solution to a problem of Katona on counting cliques of weighted graphs	2022	Peter Borg Carl Feghali Rémi Pellerin
+	A short proof of Talbot’s theorem for intersecting separated sets	2021	Peter Borg Carl Feghali
+	Isolation of k-cliques II	2021	Peter Borg Kurt Fenech Pawaton Kaemawichanurat
+ PDF Chat	Reducing the maximum degree of a graph: comparisons of bounds	2021	Peter Borg
+	Isolation of connected graphs	2021	Peter Borg
+	Reducing the maximum degree of a graph: comparisons of bounds.	2020	Peter Borg
+	Cross-intersecting subfamilies of levels of hereditary families	2020	Peter Borg
+	Isolation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e25" altimg="si20.svg"><mml:mi>k</mml:mi></mml:math>-cliques	2020	Peter Borg Kurt Fenech Pawaton Kaemawichanurat
+	Isolation of Cycles	2020	Peter Borg
+	A generalization of the Art Gallery Theorem	2020	Peter Borg Pawaton Kaemawichanurat
+	Partial domination of maximal outerplanar graphs	2020	Peter Borg Pawaton Kaemawichanurat
+	A simple proof of Talbot's theorem for intersecting separated sets	2020	Peter Borg Carl Feghali
+	The Hilton-Spencer cycle theorems via Katona's shadow intersection theorem	2020	Peter Borg Carl Feghali
+	Reducing the maximum degree of a graph: comparisons of bounds	2020	Peter Borg
+	Extensions of the Art Gallery Theorem	2020	Peter Borg Pawaton Kaemawichanurat
+	The maximum sum of sizes of cross-intersecting families of subsets of a set	2020	Peter Borg Carl Feghali
+	On the Hilton-Spencer intersection theorems for unions of cycles	2019	Peter Borg Carl Feghali
+	Partial domination of maximal outerplanar graphs	2019	Peter Borg Pawaton Kaemawichanurat
+	Cross-intersecting non-empty uniform subfamilies of hereditary families	2019	Peter Borg
+	Partial domination of maximal outerplanar graphs	2019	Peter Borg Pawaton Kaemawichanurat
+	On the Hilton-Spencer intersection theorems for unions of cycles	2019	Peter Borg Carl Feghali
+	Isolation of $k$-cliques	2018	Peter Borg Kurt Fenech Pawaton Kaemawichanurat
+	Isolation of cycles.	2018	Peter Borg
+	Irregular independence and irregular domination	2018	Peter Borg Yair Caro Kurt Fenech
+	Cross-intersecting non-empty uniform subfamilies of hereditary families	2018	Peter Borg
+	Cross-intersecting subfamilies of levels of hereditary families	2018	Peter Borg
+ PDF Chat	Intersecting families, cross-intersecting families, and a proof of a conjecture of Feghali, Johnson and Thomas	2018	Peter Borg
+ PDF Chat	Reducing the maximum degree of a graph by deleting vertices: the extremal cases	2018	Peter Borg Kurt Fenech
+	Isolation of $k$-cliques	2018	Peter Borg Kurt Fenech Pawaton Kaemawichanurat
+	Isolation of cycles	2018	Peter Borg
+	Cross-intersecting non-empty uniform subfamilies of hereditary families	2018	Peter Borg
+	Cross-intersecting subfamilies of levels of hereditary families	2018	Peter Borg
+	Irregular independence and irregular domination	2017	Peter Borg Yair Caro Kurt Fenech
+	Intersecting families, cross-intersecting families, and a proof of a conjecture of Feghali, Johnson and Thomas	2017	Peter Borg
+ PDF Chat	The maximum product of sizes of cross-intersecting families	2017	Peter Borg
+	Intersecting families, cross-intersecting families, and a proof of a conjecture of Feghali, Johnson and Thomas	2017	Peter Borg
+	Irregular independence and irregular domination	2017	Peter Borg Yair Caro Kurt Fenech
+	A Sharp Bound for the Product of Weights of Cross-Intersecting Families	2016	Peter Borg
+	Stars on trees	2016	Peter Borg
+ PDF Chat	The maximum product of weights of cross-intersecting families	2016	Peter Borg
+	The maximum product of sizes of cross-intersecting families	2016	Peter Borg
+	Stars on trees	2016	Peter Borg
+	The Katona cycle proof of the Erdős–Ko–Rado theorem and its possibilities	2016	Peter Borg Karen Meagher
+	PERMANENT VERSUS DETERMINANT, OBSTRUCTIONS,	2016	Kronecker Coefficients Peter Borg
+	The maximum product of sizes of cross-intersecting families	2016	Peter Borg
+	Stars on trees	2016	Peter Borg
+	The maximum product of weights of cross-intersecting families	2015	Peter Borg
+ PDF Chat	A cross‐intersection theorem for subsets of a set	2015	Peter Borg
+	The maximum product of weights of cross-intersecting families	2015	Peter Borg
+	Strongly intersecting integer partitions	2014	Peter Borg
+	A short proof of an Erdős–Ko–Rado theorem for compositions	2014	Peter Borg
+	Intersecting generalised permutations	2014	Peter Borg Karen Meagher
+	Intersecting generalised permutations	2014	Peter Borg Karen Meagher
+	Erdős-Ko-Rado with separation conditions.	2014	Peter Borg
+	Intersecting generalised permutations	2014	Peter Borg Karen Meagher
+	The maximum product of sizes of cross-$t$-intersecting uniform families	2013	Peter Borg
+ PDF Chat	The maximum sum and the maximum product of sizes of cross-intersecting families	2013	Peter Borg
+	A Hilton–Milner-type theorem and an intersection conjecture for signed sets	2013	Peter Borg
+	Non-trivial intersecting uniform sub-families of hereditary families	2013	Peter Borg
+	Intersecting integer partitions	2013	Peter Borg
+	Intersecting integer partitions	2013	Peter Borg
+	The maximum product of sizes of cross-$t$-intersecting uniform families	2013	Peter Borg
+	Cross-intersecting sub-families of hereditary families	2012	Peter Borg
+	Cross-intersecting integer sequences	2012	Peter Borg
+	The maximum sum and product of sizes of cross-intersecting families	2011	Peter Borg
+	Cross-intersecting sub-families of hereditary families	2011	Peter Borg
+	The maximum sum and maximum product of sizes of cross-intersecting families	2011	Peter Borg
+	The maximum sum and product of sizes of cross-intersecting families	2011	Peter Borg
+	Maximum Hitting of a Set by Compressed Intersecting Families	2011	Peter Borg
+	Intersecting families of sets and permutations: a survey	2011	Peter Borg
+	Cross-intersecting sub-families of hereditary families	2011	Peter Borg
+	The maximum sum and maximum product of sizes of cross-intersecting families	2011	Peter Borg
+	Sharp bounds for the independence number	2010	Peter Borg
+	On Chvátal’s conjecture and a conjecture on families of signed sets	2010	Peter Borg
+ PDF Chat	On Cross-Intersecting Uniform Sub-Families of Hereditary Families	2010	Peter Borg
+	Multiple cross-intersecting families of signed sets	2010	Peter Borg Imre Leader
+	A sharp upper bound for the independence number	2010	Peter Borg
+ PDF Chat	Cross-Intersecting Families of Partial Permutations	2010	Peter Borg
+ PDF Chat	Cross-intersecting families of permutations	2009	Peter Borg
+	Extremal <i>t</i> -intersecting sub-families of hereditary families	2008	Peter Borg
+	On <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>t</mml:mi></mml:math>-intersecting families of signed sets and permutations	2008	Peter Borg
+	The Erdős-Ko-Rado properties of various graphs containing singletons	2008	Peter Borg Fred Holroyd
+	The Erdős–Ko–Rado properties of set systems defined by double partitions	2008	Peter Borg Fred Holroyd
+	A short proof of a cross-intersection theorem of Hilton	2008	Peter Borg
+ PDF Chat	Intersecting and Cross-Intersecting Families of Labeled Sets	2008	Peter Borg
+ PDF Chat	Intersecting Systems of Signed Sets	2007	Peter Borg
+	Some set intersection theorems of extremal type	2007	Peter Borg
+	A basic number theoretic result	2000	Peter Borg

Common Coauthors

Coauthor	Papers Together
Pawaton Kaemawichanurat	10
Carl Feghali	9
Kurt Fenech	8
Karen Meagher	4
Yair Caro	3
Karl Bartolo	3
Dayle Scicluna	3
Rémi Pellerin	2
Fred Holroyd	2
Mercè Mora	1
Kronecker Coefficients	1
Imre Leader	1
Marı́a José Souto Salorio	1
Magdalena Lemańska	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF Chat	INTERSECTION THEOREMS FOR SYSTEMS OF FINITE SETS	1961	Péter L. Erdős Chao Ko R. Rado	37
+	Extremal <i>t</i> -intersecting sub-families of hereditary families	2008	Peter Borg	30
+	Erdös–Ko–Rado Theorem—22 Years Later	1983	Michel Deza Péter Frankl	28
+	12. The Number of Simplices in a Complex	1963	Joseph B. Kruskal	27
+	The Complete Intersection Theorem for Systems of Finite Sets	1997	Rudolf Ahlswede Levon H. Khachatrian	25
+	SOME INTERSECTION THEOREMS FOR SYSTEMS OF FINITE SETS	1967	A. J. W. Hilton E. C. Milner	24
+	Intersecting families of sets and permutations: a survey	2011	Peter Borg	23
+ PDF Chat	Graphs with the Erdős–Ko–Rado property	2005	Fred Holroyd John Talbot	22
+ PDF Chat	Intersecting families of permutations	2003	Peter J‎. Cameron Cheng Yeaw Ku	22
+ PDF Chat	Compression and Erdős–Ko–Rado graphs	2005	Fred Holroyd C. L. Spencer John Talbot	20
+	Erdös-Ko-Rado from Kruskal-Katona	1974	D. E. Daykin	20
+	A simple proof of the Erdös-Chao Ko-Rado theorem	1972	Gyula O. H. Katona	20
+	An Intersection Theorem for a Collection of Families of Subsets of a Finite Set	1977	A. J. W. Hilton	19
+ PDF Chat	Cross-intersecting families and primitivity of symmetric systems	2010	Jun Wang Huajun Zhang	17
+ PDF Chat	The maximum sum and the maximum product of sizes of cross-intersecting families	2013	Peter Borg	16
+ PDF Chat	INTERSECTING FAMILIES OF SEPARATED SETS	2003	John Talbot	16
+ PDF Chat	Cross-intersecting families of permutations	2009	Peter Borg	16
+ PDF Chat	Cross-Intersecting Families of Partial Permutations	2010	Peter Borg	16
+	A short proof of a cross-intersection theorem of Hilton	2008	Peter Borg	15
+	Multiple cross-intersecting families of signed sets	2010	Peter Borg Imre Leader	15
+	Cross-intersecting sub-families of hereditary families	2012	Peter Borg	14
+	The exact bound in the Erdős-Ko-Rado theorem for cross-intersecting families	1989	Makoto Matsumoto Norihide Tokushige	14
+	An Erdős-Ko-Rado Theorem For Signed Sets	1997	B Bollobás Imre Leader	13
+	The exact bound in the Erdös-Ko-Rado theorem	1984	Richard M. Wilson	13
+ PDF Chat	The Erdős-Ko-Rado Theorem for Integer Sequences	1999	Péter Frankl Norihide Tokushige	12
+ PDF Chat	A new generalization of the Erdős-Ko-Rado theorem	1983	Péter Frankl Zoltán Füredi	12
+	On <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>t</mml:mi></mml:math>-intersecting families of signed sets and permutations	2008	Peter Borg	12
+ PDF Chat	Intersecting Systems of Signed Sets	2007	Peter Borg	12
+	On cross t-intersecting families of sets	2010	Norihide Tokushige	11
+	Erdős–Ko–Rado theorems for simplicial complexes	2011	Russ Woodroofe	11
+ PDF Chat	A Group-Theoretic Setting for Some Intersecting Sperner Families	1992	Péter L. Erdős Ulrich Faigle Walter Kern	11
+	An Erdös-Ko-Rado theorem for the subcubes of a cube	1984	Konrad Engel	11
+	Erdős–Ko–Rado theorems for chordal graphs and trees	2010	Glenn Hurlbert Vikram Kamat	11
+ PDF Chat	Invitation to intersection problems for finite sets	2016	Péter Frankl Norihide Tokushige	11
+ PDF Chat	Intersecting and Cross-Intersecting Families of Labeled Sets	2008	Peter Borg	11
+	On the maximum number of permutations with given maximal or minimal distance	1977	Péter Frankl Mikhail Deza	10
+	An analogue of the Erdös-Ko-Rado theorem for the Hamming schemes H(n, q)	1982	Aeryung Moon	10
+	On a combinatorial conjecture of Erdös	1966	Daniel J. Kleitman	10
+	Quelques problemes concernant les cliques des hypergraphes h-complets et q-parti h-complets	1974	Jean Meyer	10
+	A new result on Chvátal's conjecture	1992	Hunter S. Snevily	10
+	Intersecting families of edges in hypergraphs having the hereditary property	1974	Vašek Chvátal	9
+	On Chvátal’s conjecture and a conjecture on families of signed sets	2010	Peter Borg	9
+ PDF Chat	A cross‐intersection theorem for subsets of a set	2015	Peter Borg	9
+	A new short proof of the EKR theorem	2012	Péter Frankl Zoltán Füredi	9
+	Stable sets of maximal size in Kneser-type graphs	2003	Benoît Larose Claudia Malvenuto	9
+ PDF Chat	Partial domination - the isolation number of a graph	2017	Yair Caro Adriana Hansberg	9
+	The eigenvalue method for cross t-intersecting families	2013	Norihide Tokushige	9
+	Intersecting families of permutations	2011	David Ellis Ehud Friedgut Haran Pilpel	8
+	An intersection theorem for weighted sets	2001	Christian Bey	8
+	A generalization of the katona theorem for crosst-intersecting families	1989	Makoto Matsumoto Norihide Tokushige	8