Reconfiguring k-colourings of Complete Bipartite Graphs

IF 0.6 Q3 MATHEMATICS

Kyungpook Mathematical Journal Pub Date : 2016-09-23 DOI:10.5666/KMJ.2016.56.3.647

Marcel Celaya, Kelly Choo, G. MacGillivray, K. Seyffarth

引用次数: 10

Abstract

Let H be a graph, and k ≥ χ(H) an integer. We say that H has a cyclic Gray code of k-colourings if and only if it is possible to list all its k-colourings in such a way that consecutive colourings, including the last and the first, agree on all vertices of H except one. The Gray code number of H is the least integer k0(H) such that H has a cyclic Gray code of its k-colourings for all k ≥ k0(H). For complete bipartite graphs, we prove that k0(K`,r) = 3 when both ` and r are odd, and k0(K`,r) = 4 otherwise.

查看原文本刊更多论文

完全二部图的k-着色的重构

设H为图，k≥χ(H)为整数。我们说H有k个着色的循环Gray编码，当且仅当有可能列出它的所有k个着色，使得连续着色，包括最后一个和第一个，在H的所有顶点上一致，除了一个。H的Gray码数是最小的整数k0(H)，使得H对所有k≥k0(H)都有其k色的循环Gray码。对于完全二部图，我们证明了当'和r都是奇数时k0(K '，r) = 3，否则k0(K '，r) = 4。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Kyungpook Mathematical Journal MATHEMATICS-

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： Kyungpook Mathematical Journal is an international journal devoted to significant research concerning all aspects of mathematics. The journal has a preference for papers having a broad interest. One volume of the journal is published every year. Each volume until volume 42 consisted of two issues; however, starting from volume 43(2003), each volume consists of four issues. Authors should strive for expository clarity and good literary style. Manuscripts should be prepared as follows. The first page must consist of a short descriptive title, followed by the name(s) and address(es) of the author(s) along with an electronic address if available.