Decomposition of multigraphs

A decomposition of Gallai multigraphs

An edge-colored cycle is rainbow if its edges are colored with distinct colors. A Gallai (multi) graph is a simple, complete, edge-colored (multi) graph lacking rainbow triangles. As has been previously shown for Gallai graphs, we show that Gallai multigraphs admit a simple iterative construction. Moreover, we show that Gallai multigraphs give rise to a surprising and highly structured decompos...

Decomposing Semi-complete Multigraphs and Directed Graphs into Paths of Length Two

A P3-decomposition of a graph is a partition of the edges of the graph into paths of length two. We give a necessary and sufficient condition for a semi-complete multigraph, that is a multigraph with at least one edge between each pair of vertices, to have a P3-decomposition. We show that this condition can be tested in strongly polynomial-time, and that the same condition applies to a larger c...

The complexity of P4-decomposition of regular graphs and multigraphs

Decompositions Of λKv Into Multigraphs With Four Vertices And Five Edges

This paper is motivated by a survey on the existence of G-designs by Adams, Bryant and Buchanan, where they gave the spectrum of the decomposition of complete graphs into graphs with small numbers of vertices. We give difference family-type constructions to decompose λ copies, where λ ≥ 2, of the complete graph K v into several multigraphs on four vertices and five edges including so called " 2...

Multigraph decomposition into stars and into multistars

We study the decomposition of multigraphs with a constant edge multiplicity into copies of a fixed starH =K1,t :We present necessary and sufficient conditions for such a decomposition to exist where t = 2 and prove NP-completeness of the corresponding decision problem for any t 3.We also prove NP-completeness when the edge multiplicity function is not restricted either on the input G or on the ...