Anti-van der Waerden Numbers of Some 2-Connected Outerplanar Graphs
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Published:2024-04-06
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Volume:
Page:
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ISSN:0219-2659
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Container-title:Journal of Interconnection Networks
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language:en
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Short-container-title:J. Inter. Net.
Author:
Feng Xinge1ORCID,
Deng Xingchao1ORCID,
Cai Junqing1ORCID
Affiliation:
1. College of Mathematical Science, Tianjin Normal University, Tianjin City 300071, P. R. China
Abstract
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].
Funder
Tianjin Normal University Research Innovation Project for Postgraduate Students, China
Publisher
World Scientific Pub Co Pte Ltd