Decompositions of multigraphs into parts with two edges

Jaroslav Ivančo; Mariusz Meszka; Zdzisław Skupień

Discussiones Mathematicae Graph Theory (2002)

  • Volume: 22, Issue: 1, page 113-121
  • ISSN: 2083-5892

Abstract

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Given a family 𝓕 of multigraphs without isolated vertices, a multigraph M is called 𝓕-decomposable if M is an edge disjoint union of multigraphs each of which is isomorphic to a member of 𝓕. We present necessary and sufficient conditions for the existence of such decompositions if 𝓕 comprises two multigraphs from the set consisting of a 2-cycle, a 2-matching and a path with two edges.

How to cite

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Jaroslav Ivančo, Mariusz Meszka, and Zdzisław Skupień. "Decompositions of multigraphs into parts with two edges." Discussiones Mathematicae Graph Theory 22.1 (2002): 113-121. <http://eudml.org/doc/270217>.

@article{JaroslavIvančo2002,
abstract = {Given a family 𝓕 of multigraphs without isolated vertices, a multigraph M is called 𝓕-decomposable if M is an edge disjoint union of multigraphs each of which is isomorphic to a member of 𝓕. We present necessary and sufficient conditions for the existence of such decompositions if 𝓕 comprises two multigraphs from the set consisting of a 2-cycle, a 2-matching and a path with two edges.},
author = {Jaroslav Ivančo, Mariusz Meszka, Zdzisław Skupień},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {edge decomposition; multigraph; line graph; 1-factor},
language = {eng},
number = {1},
pages = {113-121},
title = {Decompositions of multigraphs into parts with two edges},
url = {http://eudml.org/doc/270217},
volume = {22},
year = {2002},
}

TY - JOUR
AU - Jaroslav Ivančo
AU - Mariusz Meszka
AU - Zdzisław Skupień
TI - Decompositions of multigraphs into parts with two edges
JO - Discussiones Mathematicae Graph Theory
PY - 2002
VL - 22
IS - 1
SP - 113
EP - 121
AB - Given a family 𝓕 of multigraphs without isolated vertices, a multigraph M is called 𝓕-decomposable if M is an edge disjoint union of multigraphs each of which is isomorphic to a member of 𝓕. We present necessary and sufficient conditions for the existence of such decompositions if 𝓕 comprises two multigraphs from the set consisting of a 2-cycle, a 2-matching and a path with two edges.
LA - eng
KW - edge decomposition; multigraph; line graph; 1-factor
UR - http://eudml.org/doc/270217
ER -

References

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  1. [1] K. Bryś, M. Kouider, Z. Lonc and M. Mahéo, Decomposition of multigraphs, Discuss. Math. Graph Theory 18 (1998) 225-232, doi: 10.7151/dmgt.1078. Zbl0926.05028
  2. [2] Y. Caro, The decomposition of graphs into graphs having two edges, a manuscript. 
  3. [3] Y. Caro and J. Schönheim, Decompositions of trees into isomorphic subtrees, Ars Comb. 9 (1980) 119-130. Zbl0454.05022
  4. [4] J. Ivančo, M. Meszka and Z. Skupień; Decomposition of multigraphs into isomorphic graphs with two edges, Ars Comb. 51 (1999) 105-112. 
  5. [5] E.B. Yavorski, Representations of oriented graphs and φ-transformations [Russian], in: A. N. Sarkovski, ed., Theoretical and Applied Problems of Differential Equations and Algebra [Russian] (Nauk. Dumka, Kiev, 1978) 247-250. 
  6. [6] M. Las Vergnas, A note on matchings in graphs, Cahiers Centre Etudes Rech. Opér. 17 (1975) 257-260. 
  7. [7] Z. Skupień; Problem 270 [on 2-edge-decomposable multigraphs], Discrete Math. 164 (1997) 320-321. 
  8. [8] D.P. Sumner, Graphs with 1-factors, Proc. Amer. Math. Soc. 42 (1974) 8-12. Zbl0293.05157

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