Coloring Graphs with Dense Neighborhoods

被引：5
|
作者：
Rabern, Landon [1 ]
机构：
[1] LBD Data, Orange, CT 06477 USA
来源：
JOURNAL OF GRAPH THEORY | 2014年 / 76卷 / 04期
关键词：
coloring; dense; Reed's conjecture; Borodin-Kostochka conjecture; Brooks' theorem; TRANSVERSALS;
D O I：
10.1002/jgt.21768
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
It is shown that any graph with maximum degree in which the average degree of the induced subgraph on the set of all neighbors of each vertex exceeds 6k26k2+1+k+6 is either (-k)-colorable or contains a clique on more than -2k vertices. In the k=1 case we improve the bound on the average degree to 23+4 and the bound on the clique number to -1. As corollaries, we show that every graph satisfies max{,-1,4} and every graph satisfies max{,-1,remvoe15+48n+734}.
引用
收藏
页码：323 / 340
页数：18
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