Chromatic Number and Orientations of Graphs and Signed Graphs
Chromatic Number and Orientations of Graphs and Signed Graphs
Assume $D$ is a digraph, and $D'$ is a spanning sub-digraph of $D$. We say $D'$ is a modulo-$k$ Eulerian sub-digraph of $D$ if for each vertex $v$ of $D'$, $d_{D'}^+(v) \equiv d_{D'}^-(v) \pmod{k}$. A modulo-$k$ Eulerian sub-digraph $D'$ of $D$ is special if for every vertex $v$, $d_D^+(v) = …