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

Xinge Feng,Xingchao Deng,Junqing Cai

JOURNAL OF INTERCONNECTION NETWORKS（2024）

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Abstract
Given a graph G and a positive integer k, the anti-van der Waerden number aw(G,k) is defined as the minimum positive integer r such that every exact r-coloring of the vertices of G admits a rainbow k-AP. In this paper, we determine the exact value of aw(G, 3) if G is a 2-connected outerplanar graph with diameters 2, 3.
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Key words
Anti-van der Waerden number,outerplanar graph,rainbow arithmetic progression
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