Ramsey-Type Results for Path Covers and Path Partitions
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Published:2022-10-07
Issue:4
Volume:29
Page:
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ISSN:1077-8926
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Container-title:The Electronic Journal of Combinatorics
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language:
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Short-container-title:Electron. J. Combin.
Author:
Chiba Shuya,Furuya Michitaka
Abstract
A family $\mathcal{P}$ of subgraphs of $G$ is called a path cover (resp. a path partition) of $G$ if $\bigcup _{P\in \mathcal{P}}V(P)=V(G)$ (resp. $\dot\bigcup _{P\in \mathcal{P}}V(P)=V(G)$) and every element of $\mathcal{P}$ is a path. The minimum cardinality of a path cover (resp. a path partition) of $G$ is denoted by ${\rm pc}(G)$ (resp. ${\rm pp}(G)$). In this paper, we characterize the forbidden subgraph conditions assuring us that ${\rm pc}(G)$ (or ${\rm pp}(G)$) is bounded by a constant. Our main results introduce a new Ramsey-type problem.
Publisher
The Electronic Journal of Combinatorics
Subject
Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics
Cited by
1 articles.
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