On total 9-coloring planar graphs of maximum degree seven
نویسندگان
چکیده
Given a graphG, a total k-coloring ofG is a simultaneous coloring of the vertices and edges ofGwith at most k colors. If ∆(G) is themaximum degree ofG, then no graph has a total ∆-coloring, but Vizing conjectured that every graph has a total (∆ + 2)-coloring. This Total Coloring Conjecture remains open even for planar graphs. This article proves one of the two remaining planar cases, showing that every planar (and projective) graph with ∆ ≤ 7 has a total 9-coloring by means of the discharging method. c © 1999 John Wiley & Sons, Inc. J Graph Theory 31: 67–73, 1999
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ورودعنوان ژورنال:
- Journal of Graph Theory
دوره 31 شماره
صفحات -
تاریخ انتشار 1999