### 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 | |

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

### Cite this

*Discrete Mathematics*,

*340*(2), 87-95. https://doi.org/10.1016/j.disc.2016.07.015

**Degree sum conditions for path-factors with specified end vertices in bipartite graphs.** / Matsubara, Ryota; Matsumura, Hajime; Tsugaki, Masao; Yamashita, Tomoki.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 340, no. 2, pp. 87-95. https://doi.org/10.1016/j.disc.2016.07.015

}

TY - JOUR

T1 - Degree sum conditions for path-factors with specified end vertices in bipartite graphs

AU - Matsubara, Ryota

AU - Matsumura, Hajime

AU - Tsugaki, Masao

AU - Yamashita, Tomoki

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

UR - http://www.scopus.com/inward/record.url?scp=84984832848&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84984832848&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2016.07.015

DO - 10.1016/j.disc.2016.07.015

M3 - Article

AN - SCOPUS:84984832848

VL - 340

SP - 87

EP - 95

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 2

ER -