Graph decompositions and D3-paths with a prescribed endvertex

Hikoe Enomoto, Shinsuke Matsunaga, Katsuhiro Ota

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Let k and n be positive integers. Let G be a graph of order n≤4k, and let n = ∑k i=1 ai be a partition of n into k positive integers ai with 1≤ai≤4. In Matsunaga (Preprint, 1995) one of the authors proved that if G is 2-connected and the minimum degree of G is at least k, then with certain types of exceptions being allowed, the vertex set of G can be decomposed into k disjoint subsets Al,...,Ak so that |Ai| = ai and "the subgraph induced by Ai is connected" for all i, 1≤i≤k. In the present paper we extend this result for connected graphs in general. The paper also features the existence of D3-paths with a prescribed endvertex in a graph. (A D3-path in a graph is a path of the graph whose removal leaves no component of order at least 3.)

Original languageEnglish
Pages (from-to)87-104
Number of pages18
JournalDiscrete Mathematics
Volume213
Issue number1-3
Publication statusPublished - 2000 Feb 28

Fingerprint

Graph Decomposition
Decomposition
Path
Graph in graph theory
Integer
Minimum Degree
Induced Subgraph
Exception
Connected graph
Disjoint
Partition
Subset
Vertex of a graph

Keywords

  • D-path
  • Graph decomposition

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Graph decompositions and D3-paths with a prescribed endvertex. / Enomoto, Hikoe; Matsunaga, Shinsuke; Ota, Katsuhiro.

In: Discrete Mathematics, Vol. 213, No. 1-3, 28.02.2000, p. 87-104.

Research output: Contribution to journalArticle

Enomoto, H, Matsunaga, S & Ota, K 2000, 'Graph decompositions and D3-paths with a prescribed endvertex', Discrete Mathematics, vol. 213, no. 1-3, pp. 87-104.
Enomoto, Hikoe ; Matsunaga, Shinsuke ; Ota, Katsuhiro. / Graph decompositions and D3-paths with a prescribed endvertex. In: Discrete Mathematics. 2000 ; Vol. 213, No. 1-3. pp. 87-104.
@article{10469b5ef3954bd5ac603befff6e2a8b,
title = "Graph decompositions and D3-paths with a prescribed endvertex",
abstract = "Let k and n be positive integers. Let G be a graph of order n≤4k, and let n = ∑k i=1 ai be a partition of n into k positive integers ai with 1≤ai≤4. In Matsunaga (Preprint, 1995) one of the authors proved that if G is 2-connected and the minimum degree of G is at least k, then with certain types of exceptions being allowed, the vertex set of G can be decomposed into k disjoint subsets Al,...,Ak so that |Ai| = ai and {"}the subgraph induced by Ai is connected{"} for all i, 1≤i≤k. In the present paper we extend this result for connected graphs in general. The paper also features the existence of D3-paths with a prescribed endvertex in a graph. (A D3-path in a graph is a path of the graph whose removal leaves no component of order at least 3.)",
keywords = "D-path, Graph decomposition",
author = "Hikoe Enomoto and Shinsuke Matsunaga and Katsuhiro Ota",
year = "2000",
month = "2",
day = "28",
language = "English",
volume = "213",
pages = "87--104",
journal = "Discrete Mathematics",
issn = "0012-365X",
publisher = "Elsevier",
number = "1-3",

}

TY - JOUR

T1 - Graph decompositions and D3-paths with a prescribed endvertex

AU - Enomoto, Hikoe

AU - Matsunaga, Shinsuke

AU - Ota, Katsuhiro

PY - 2000/2/28

Y1 - 2000/2/28

N2 - Let k and n be positive integers. Let G be a graph of order n≤4k, and let n = ∑k i=1 ai be a partition of n into k positive integers ai with 1≤ai≤4. In Matsunaga (Preprint, 1995) one of the authors proved that if G is 2-connected and the minimum degree of G is at least k, then with certain types of exceptions being allowed, the vertex set of G can be decomposed into k disjoint subsets Al,...,Ak so that |Ai| = ai and "the subgraph induced by Ai is connected" for all i, 1≤i≤k. In the present paper we extend this result for connected graphs in general. The paper also features the existence of D3-paths with a prescribed endvertex in a graph. (A D3-path in a graph is a path of the graph whose removal leaves no component of order at least 3.)

AB - Let k and n be positive integers. Let G be a graph of order n≤4k, and let n = ∑k i=1 ai be a partition of n into k positive integers ai with 1≤ai≤4. In Matsunaga (Preprint, 1995) one of the authors proved that if G is 2-connected and the minimum degree of G is at least k, then with certain types of exceptions being allowed, the vertex set of G can be decomposed into k disjoint subsets Al,...,Ak so that |Ai| = ai and "the subgraph induced by Ai is connected" for all i, 1≤i≤k. In the present paper we extend this result for connected graphs in general. The paper also features the existence of D3-paths with a prescribed endvertex in a graph. (A D3-path in a graph is a path of the graph whose removal leaves no component of order at least 3.)

KW - D-path

KW - Graph decomposition

UR - http://www.scopus.com/inward/record.url?scp=0043284116&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0043284116&partnerID=8YFLogxK

M3 - Article

VL - 213

SP - 87

EP - 104

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -