一些 2 连接外平面图的反范德瓦登数

Pub Date : 2024-04-06 DOI:10.1142/s0219265924500051

Xin Feng, Xingchao Deng, Junqing Cai

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引用次数: 0

摘要

给定一个图[式：见正文]和一个正整数[式：见正文]，反范德瓦登数[式：见正文]被定义为[式：见正文]的最小正整数[式：见正文]，使得[式：见正文]顶点的每一个精确[式：见正文]着色都允许一个彩虹[式：见正文]-AP。在本文中，如果[公式：见正文]是一个直径为[公式：见正文]的[公式：见正文]连接外平面图，我们将确定[公式：见正文]的精确值。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Anti-van der Waerden Numbers of Some 2-Connected Outerplanar Graphs

Given a graph [Formula: see text] and a positive integer [Formula: see text], the anti-van der Waerden number [Formula: see text] is defined as the minimum positive integer [Formula: see text] such that every exact [Formula: see text]-coloring of the vertices of [Formula: see text] admits a rainbow [Formula: see text]-AP. In this paper, we determine the exact value of [Formula: see text] if [Formula: see text] is a [Formula: see text]-connected outerplanar graph with diameters [Formula: see text].

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