Decompositions of multigraphs into parts with two edges

Jaroslav Ivančo; Mariusz Meszka; Zdzisław Skupień

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$H$ -decompositions of $r$ -graphs when $H$ is an $r$ -graph with exactly 2 edges.

Sousa, Teresa (2010)

The Electronic Journal of Combinatorics [electronic only]

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Moves Without Forbidden Transitions in a Graph

Anton Kotzig (1968)

Matematický časopis

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Decompositions of multigraphs into parts with the same size

Jaroslav Ivanco (2010)

Discussiones Mathematicae Graph Theory

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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 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...