树的边缘预着色扩展Ⅱ

IF 0.5 4区 数学 Q3 MATHEMATICS
C. J. Casselgren, F. B. Petros
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引用次数: 3

摘要

摘要我们考虑了树的局部边缘着色的扩展和避免问题;即,给定树T的部分边着色φ,我们感兴趣的是,在φ下着色的每条边上,是否存在与着色φ一致的适当Δ(T)-边着色;或者,类似地,如果在φ下着色的每条边上都有一个与φ不一致的适当Δ(T)-边着色。我们描述了树T中具有最多Δ(T)+1个预着色边的部分边着色是可扩展的,从而证明了Andersen对拉丁正方形的结果的类似性。此外,我们还得到了一些关于扩展部分边着色的“混合”结果,条件是该扩展应避免给定的部分边着色;特别地,对于所有0≤k≤Δ(T),我们刻画了由树T的Δ(T。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Edge Precoloring Extension of Trees II
Abstract We consider the problem of extending and avoiding partial edge colorings of trees; that is, given a partial edge coloring φ of a tree T we are interested in whether there is a proper Δ(T )-edge coloring of T that agrees with the coloring φ on every edge that is colored under φ; or, similarly, if there is a proper Δ(T )-edge coloring that disagrees with φ on every edge that is colored under φ. We characterize which partial edge colorings with at most Δ(T ) + 1 precolored edges in a tree T are extendable, thereby proving an analogue of a result by Andersen for Latin squares. Furthermore we obtain some “mixed” results on extending a partial edge coloring subject to the condition that the extension should avoid a given partial edge coloring; in particular, for all 0 ≤ k ≤ Δ(T ), we characterize for which configurations consisting of a partial coloring φ of Δ(T ) − k edges and a partial coloring ψ of k + 1 edges of a tree T, there is an extension of φ that avoids ψ.
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来源期刊
CiteScore
2.20
自引率
0.00%
发文量
22
审稿时长
53 weeks
期刊介绍: The Discussiones Mathematicae Graph Theory publishes high-quality refereed original papers. Occasionally, very authoritative expository survey articles and notes of exceptional value can be published. The journal is mainly devoted to the following topics in Graph Theory: colourings, partitions (general colourings), hereditary properties, independence and domination, structures in graphs (sets, paths, cycles, etc.), local properties, products of graphs as well as graph algorithms related to these topics.
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