Total coloring of claw-free planar graphs
Copyright policy )Total coloring of claw-free planar graphs
The total coloring conjecture (TCC) is an important conjecture in the field of graph coloring, which has been widely studied in the literature. So far TCC has been confirmed for graphs with \(\Delta\leq 5\) and for planar graphs with \(\Delta\geq 7\). Therefore, the only open case for planar graphs is \(\Delta=6\). In this paper, the author proves that TCC holds for claw-free planar graphs with \(\Delta=6\). In my opinion, the result is meaningful and interesting, which partially supports the correctness of TCC.
planar graph, claw, total coloring conjecture, planar graphs, Planar graphs; geometric and topological aspects of graph theory, total coloring, Coloring of graphs and hypergraphs, 05c15, QA1-939, Mathematics
planar graph, claw, total coloring conjecture, planar graphs, Planar graphs; geometric and topological aspects of graph theory, total coloring, Coloring of graphs and hypergraphs, 05c15, QA1-939, Mathematics
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