# 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

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topJaroslav 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

top- [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] Y. Caro, The decomposition of graphs into graphs having two edges, a manuscript.
- [3] Y. Caro and J. Schönheim, Decompositions of trees into isomorphic subtrees, Ars Comb. 9 (1980) 119-130. Zbl0454.05022
- [4] J. Ivančo, M. Meszka and Z. Skupień; Decomposition of multigraphs into isomorphic graphs with two edges, Ars Comb. 51 (1999) 105-112.
- [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] M. Las Vergnas, A note on matchings in graphs, Cahiers Centre Etudes Rech. Opér. 17 (1975) 257-260.
- [7] Z. Skupień; Problem 270 [on 2-edge-decomposable multigraphs], Discrete Math. 164 (1997) 320-321.
- [8] D.P. Sumner, Graphs with 1-factors, Proc. Amer. Math. Soc. 42 (1974) 8-12. Zbl0293.05157

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