Adjacent strong edge colorings and total colorings of regular graphs
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It is conjectured that X as ′ (G) = X t (G) for every k-regular graph G with no C 5 component (k ⩾ 2). This conjecture is shown to be true for many classes of graphs, including: graphs of type 1; 2-regular, 3-regular and (|V(G)| - 2)-regular graphs; bipartite graphs; balanced complete multipartite graphs; k-cubes; and joins of two matchings or cycles.
Keywordsgraph total coloring adjacent strong edge coloring
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