A new upper bound for the independence number of edge chromatic critical graphs

Vizing conjectured that every edge chromatic critical graph contains a 2-factor. Believing that stronger properties hold for this class of graphs, Luo and Zhao (2013) showed that every edge chromatic critical graph of order n with maximum degree at ...

In the study of edge colorings of ordinary graphs, Vizing’s adjacency lemma plays a crucial role. In this paper, we extend Vizing’s adjacency lemma to critical signed graphs with even maximum degrees. As an application, we show that the signed ...

An adjacent vertex-distinguishing edge coloring of a simple graph G is a proper edge coloring of G such that incident edge sets of any two adjacent vertices are assigned different sets of colors. A total coloring of a graph G is a coloring of both the ...