### Abstract

For a graph G, let σ_{2}(G) denote the minimum degree sum of a pair of nonadjacent vertices. We conjecture that if |V(G)| = n = Σ^{k}
_{i=1} a_{i} and σ_{2}(G) ≥ n+k - 1, then for any k vertices v_{1}, v_{2}, . . . , v_{k} in G, there exist vertex-disjoint paths P_{1}, P_{2}, . . ., P_{k} such that

Original language | English |
---|---|

Pages (from-to) | 163-169 |

Number of pages | 7 |

Journal | Journal of Graph Theory |

Volume | 34 |

Issue number | 2 |

Publication status | Published - 2000 Jun |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Journal of Graph Theory*,

*34*(2), 163-169.

**Partitions of a graph into paths with prescribed endvertices and lengths.** / Enomoto, Hikoe; Ota, Katsuhiro.

Research output: Contribution to journal › Article

*Journal of Graph Theory*, vol. 34, no. 2, pp. 163-169.

}

TY - JOUR

T1 - Partitions of a graph into paths with prescribed endvertices and lengths

AU - Enomoto, Hikoe

AU - Ota, Katsuhiro

PY - 2000/6

Y1 - 2000/6

N2 - For a graph G, let σ2(G) denote the minimum degree sum of a pair of nonadjacent vertices. We conjecture that if |V(G)| = n = Σk i=1 ai and σ2(G) ≥ n+k - 1, then for any k vertices v1, v2, . . . , vk in G, there exist vertex-disjoint paths P1, P2, . . ., Pk such that

AB - For a graph G, let σ2(G) denote the minimum degree sum of a pair of nonadjacent vertices. We conjecture that if |V(G)| = n = Σk i=1 ai and σ2(G) ≥ n+k - 1, then for any k vertices v1, v2, . . . , vk in G, there exist vertex-disjoint paths P1, P2, . . ., Pk such that

UR - http://www.scopus.com/inward/record.url?scp=0034197810&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034197810&partnerID=8YFLogxK

M3 - Article

VL - 34

SP - 163

EP - 169

JO - Journal of Graph Theory

JF - Journal of Graph Theory

SN - 0364-9024

IS - 2

ER -