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arXiv · 2108.07890

Constructing Triangle Decomposable Multigraphs with Minimum Multi-edges

C. M. Mynhardt·A. K. Wright
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Abstract

We study triangle decompositions of graphs. We consider constructions of classes of graphs where every edge lies on a triangle and the addition of the minimum number of multiple edges between already adjacent vertices results in a strongly triangle divisible graph that is also triangle decomposable. We explore several classes of planar graphs as well as a class of toroidal graphs.

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C. M. Mynhardt, A. K. Wright. 2021-08-19. Constructing Triangle Decomposable Multigraphs with Minimum Multi-edges. https://arxiv.org/abs/2108.07890

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