Degree sum conditions for path-factors with specified end vertices in bipartite graphs

Ryota Matsubara; Hajime Matsumura; Masao Tsugaki; Tomoki Yamashita

doi:10.1016/j.disc.2016.07.015

Degree sum conditions for path-factors with specified end vertices in bipartite graphs

Ryota Matsubara, Hajime Matsumura, Masao Tsugaki, Tomoki Yamashita

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

Let G be a graph, and let S be a subset of the vertex set of G. We denote the set of the end vertices of a path P by end(P). A path P is an S-path if |V(P)|≥2 and V(P)∩S=end(P). An S-path-system is a graph H such that H contains all vertices of S and every component of H is an S-path. In this paper, we give a sharp degree sum condition for a bipartite graph to have a spanning S-path-system.

Original language	English
Pages (from-to)	87-95
Number of pages	9
Journal	Discrete Mathematics
Volume	340
Issue number	2
DOIs	https://doi.org/10.1016/j.disc.2016.07.015
Publication status	Published - 2017 Feb 6

Keywords

Bipartite graph
Degree sum condition
Path-factor

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2016.07.015

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title = "Degree sum conditions for path-factors with specified end vertices in bipartite graphs",

abstract = "Let G be a graph, and let S be a subset of the vertex set of G. We denote the set of the end vertices of a path P by end(P). A path P is an S-path if |V(P)|≥2 and V(P)∩S=end(P). An S-path-system is a graph H such that H contains all vertices of S and every component of H is an S-path. In this paper, we give a sharp degree sum condition for a bipartite graph to have a spanning S-path-system.",

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AU - Matsubara, Ryota

AU - Matsumura, Hajime

AU - Tsugaki, Masao

AU - Yamashita, Tomoki

N1 - Funding Information: The lastauthor was supported by JSPS KAKENHI Grant Number 24740074 .

PY - 2017/2/6

Y1 - 2017/2/6

N2 - Let G be a graph, and let S be a subset of the vertex set of G. We denote the set of the end vertices of a path P by end(P). A path P is an S-path if |V(P)|≥2 and V(P)∩S=end(P). An S-path-system is a graph H such that H contains all vertices of S and every component of H is an S-path. In this paper, we give a sharp degree sum condition for a bipartite graph to have a spanning S-path-system.

AB - Let G be a graph, and let S be a subset of the vertex set of G. We denote the set of the end vertices of a path P by end(P). A path P is an S-path if |V(P)|≥2 and V(P)∩S=end(P). An S-path-system is a graph H such that H contains all vertices of S and every component of H is an S-path. In this paper, we give a sharp degree sum condition for a bipartite graph to have a spanning S-path-system.

KW - Bipartite graph

KW - Degree sum condition

KW - Path-factor

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