Decomposition of multigraphs

Mekkia Kouider; Maryvonne Mahéo; Krzysztof Bryś; Zbigniew Lonc

Discussiones Mathematicae Graph Theory (1998)

  • Volume: 18, Issue: 2, page 225-232
  • ISSN: 2083-5892

Abstract

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In this note, we consider the problem of existence of an edge-decomposition of a multigraph into isomorphic copies of 2-edge paths K 1 , 2 . We find necessary and sufficient conditions for such a decomposition of a multigraph H to exist when (i) either H does not have incident multiple edges or (ii) multiplicities of the edges in H are not greater than two. In particular, we answer a problem stated by Z. Skupień.

How to cite

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Mekkia Kouider, et al. "Decomposition of multigraphs." Discussiones Mathematicae Graph Theory 18.2 (1998): 225-232. <http://eudml.org/doc/270489>.

@article{MekkiaKouider1998,
abstract = {In this note, we consider the problem of existence of an edge-decomposition of a multigraph into isomorphic copies of 2-edge paths $K_\{1,2\}$. We find necessary and sufficient conditions for such a decomposition of a multigraph H to exist when (i) either H does not have incident multiple edges or (ii) multiplicities of the edges in H are not greater than two. In particular, we answer a problem stated by Z. Skupień.},
author = {Mekkia Kouider, Maryvonne Mahéo, Krzysztof Bryś, Zbigniew Lonc},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {edge decomposition; multigraph; perfect matching; edge-decomposition},
language = {eng},
number = {2},
pages = {225-232},
title = {Decomposition of multigraphs},
url = {http://eudml.org/doc/270489},
volume = {18},
year = {1998},
}

TY - JOUR
AU - Mekkia Kouider
AU - Maryvonne Mahéo
AU - Krzysztof Bryś
AU - Zbigniew Lonc
TI - Decomposition of multigraphs
JO - Discussiones Mathematicae Graph Theory
PY - 1998
VL - 18
IS - 2
SP - 225
EP - 232
AB - In this note, we consider the problem of existence of an edge-decomposition of a multigraph into isomorphic copies of 2-edge paths $K_{1,2}$. We find necessary and sufficient conditions for such a decomposition of a multigraph H to exist when (i) either H does not have incident multiple edges or (ii) multiplicities of the edges in H are not greater than two. In particular, we answer a problem stated by Z. Skupień.
LA - eng
KW - edge decomposition; multigraph; perfect matching; edge-decomposition
UR - http://eudml.org/doc/270489
ER -

References

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  1. [B] J.A. Bondy, Perfect Path Double Covers of Graphs, J. Graph Theory 14 (1990) 259-272, doi: 10.1002/jgt.3190140213. Zbl0745.05038
  2. [IMS] J. Ivančo, M. Meszka and Z. Skupień, Decomposition of multigraphs into isomorphic graphs with two edges, to appear in Ars Combinatoria. Zbl0977.05099
  3. [T] W.T. Tutte, The factorisation of linear graphs, J. London Math. Society 22 (1947) 107-111, doi: 10.1112/jlms/s1-22.2.107. Zbl0029.23301

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