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MINIMAX DEGREES OF QUASIPLANAR GRAPHS WITH NO SHORT CYCLES OTHER THAN TRIANGLES
2008
Taiwanese journal of mathematics
For an edge xy, let M (xy) be the maximum of the degrees of x and y. The minimax degree (or M -degree) of a graph G is M * (G) = min{M (xy)|xy ∈ E(G)}. In order to get upper bounds on the game chromatic number of planar graphs, He, Hou, Lih, Shao, Wang, and Zhu showed that every planar graph G without leaves and 4-cycles has minimax degree at most 8, which was improved by Borodin, Kostochka, Sheikh, and Yu to the sharp bound 7. We show that every planar graph G without leaves and 4-and 5-cycles
doi:10.11650/twjm/1500404982
fatcat:t74n574o6rgu7ojhecmrrgusrq