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Triangle Decompositions of Planar Graphs

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Mynhardt C. M., Bommel C. M. v.

Discussiones Mathematicae Graph Theory

2016

tom 36

nr 3

643-659

A multigraph G is triangle decomposable if its edge set can be partitioned into subsets, each of which induces a triangle of G, and rationally triangle decomposable if its triangles can be assigned rational weights such that for each edge e of G, the sum of the weights of the triangles that contain e equals 1. We present a necessary and sufficient condition for a planar multigraph to be triangle decomposable. We also show that if a simple planar graph is rationally triangle decomposable, then it has such a decomposition using only weights 0, 1 and 1/2 . This result provides a characterization of rationally triangle decomposable simple planar graphs. Finally, if G is a multigraph with K4 as underlying graph, we give necessary and sufficient conditions on the multiplicities of its edges for G to be triangle and rationally triangle decomposable.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Bommel C. M. v.

1 Mynhardt C. M.

1 2016

Wyniki wyszukiwania

Triangle Decompositions of Planar Graphs