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Constructing Triangle Decomposable Multigraphs with Minimum Multi-edges

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arxiv 2108.07890 v2 pith:3WNXVID5 submitted 2021-08-17 math.CO

C. M. Mynhardt , A. K. Wright This is my paper · ORCID
classification math.CO
keywords trianglegraphsclassesdecomposableminimumadditionadjacentalready
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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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