# Decompositions of multigraphs into parts with the same size

Discussiones Mathematicae Graph Theory (2010)

- Volume: 30, Issue: 2, page 335-347
- ISSN: 2083-5892

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topJaroslav Ivanco. "Decompositions of multigraphs into parts with the same size." Discussiones Mathematicae Graph Theory 30.2 (2010): 335-347. <http://eudml.org/doc/270804>.

@article{JaroslavIvanco2010,

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 existence of such decompositions if ℱ consists of all multigraphs of size q except for one. Namely, for a multigraph H of size q we find each multigraph M of size kq, such that every partition of the edge set of M into parts of cardinality q contains a part which induces a submultigraph of M isomorphic to H.},

author = {Jaroslav Ivanco},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {edge decompositions; multigraphs},

language = {eng},

number = {2},

pages = {335-347},

title = {Decompositions of multigraphs into parts with the same size},

url = {http://eudml.org/doc/270804},

volume = {30},

year = {2010},

}

TY - JOUR

AU - Jaroslav Ivanco

TI - Decompositions of multigraphs into parts with the same size

JO - Discussiones Mathematicae Graph Theory

PY - 2010

VL - 30

IS - 2

SP - 335

EP - 347

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 existence of such decompositions if ℱ consists of all multigraphs of size q except for one. Namely, for a multigraph H of size q we find each multigraph M of size kq, such that every partition of the edge set of M into parts of cardinality q contains a part which induces a submultigraph of M isomorphic to H.

LA - eng

KW - edge decompositions; multigraphs

UR - http://eudml.org/doc/270804

ER -

## References

top- [1] J. Ivanco, M. Meszka and Z. Skupień, Decompositions of multigraphs into parts with two edges, Discuss. Math. Graph Theory 22 (2002) 113-121, doi: 10.7151/dmgt.1162. Zbl1018.05086
- [2] W. Wang and K. Zhang, Equitable colorings of line graphs and complete r-partite graphs, Systems Science and Math. Sciences 13 (2000) 190-194. Zbl0979.05048

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