PARITY VERTEX COLORINGS OF BINOMIAL TREES

被引：4

作者：

Gregor, Petr ^{[1
]}

Skrekovski, Riste ^{[2
]}

机构：

[1] Charles Univ Prague, Dept Theoret Comp Sci & Math Log, Malostranske Nam 25, CR-11800 Prague, Czech Republic

[2] Univ Ljubljana, Dept Math, Ljubljana 1000, Slovenia

来源：

DISCUSSIONES MATHEMATICAE GRAPH THEORY | 2012年 / 32卷 / 01期

关键词：

binomial tree; parity coloring; vertex ranking;

D O I：

10.7151/dmgt.1595

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show for every k >= 1 that the binomial tree of order 3k has a vertex-coloring with 2k + 1 colors such that every path contains some color odd number of times. This disproves a conjecture from [1] asserting that for every tree T the minimal number of colors in a such coloring of T is at least the vertex ranking number of T minus one.

引用

页码：177 / 180

页数：4

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