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• # Artykuł - szczegóły

## Discussiones Mathematicae Graph Theory

2016 | 36 | 3 | 643-659

## Triangle Decompositions of Planar Graphs

EN

### Abstrakty

EN
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.

EN

643-659

wydano
2016-08-01
otrzymano
2015-04-15
poprawiono
2015-10-06
zaakceptowano
2015-10-06
online
2016-07-06

### Twórcy

• Department of Mathematics and Statistics University of Victoria P.O. Box 1700 STN CSC Victoria, BC, Canada V8W 2Y2
• Department of Mathematics and Statistics University of Victoria P.O. Box 1700 STN CSC Victoria, BC, Canada V8W 2Y2, PhD student, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, ON, Canada

### Bibliografia

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