# DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

# IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

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# Discussiones Mathematicae Graph Theory

## DECOMPOSITIONS OF MULTIGRAPHS INTO PARTS WITH TWO EDGES

 Jaroslav Ivanco Department of Geometry and Algebra Saf࠲ik University Jesennߠ5, 041 54 Košice, Slovakia e-mail: ivanco@duro.upjs.sk Mariusz Meszka and Zdzisław Skupień Faculty of Applied Mathematics AGH University of Mining and Metallurgy al. Mickiewicza 30, 30-059 Krakಷ, Poland e-mail: grmeszka@cyf-kr.edu.pl e-mail: skupien@uci.agh.edu.pl

## 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.

Keywords: edge decomposition, multigraph, line graph, 1-factor.

2000 Mathematics Subject Classification: 05C70.

## References

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