Arbitrary partitionability of product graphs

Fengxia Liu, Xirinay Nurmamat and Panpan Zhang

Applied Mathematics and Computation, 2021, vol. 408, issue C

Abstract: A graph G of order n is called arbitrarily partitionable (AP, for short) if for every sequence λ=(λ1,λ2,…,λk) of positive integers such that Σi=1kλi=n, there exists a partition (V1,V2,…,Vk) of the vertex set V(G) such that |Vi|=λi, and the subgraph G[Vi] induced by Vi is connected, for all i∈[1,k]. In this paper, we mainly discuss the arbitrary partitionability of product graphs. For the Direct product of H×Cn, we study the arbitrarily partitionability for H∈{Pm,Cm,K1,m}. For the Cartesian product, we study the arbitrarily partitionability of K1,m□Pn.

Keywords: Arbitrarily partitionable graphs; Direct product of graphs; Cartesian product of graphs; Traceable graphs (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:408:y:2021:i:c:s009630032100309x

DOI: 10.1016/j.amc.2021.126219

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