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arXiv · 1611.10058

Non-Crossing Perfect Matchings and Triangle-Free Geometric Graphs

Hazim Michman Trao·Gek L. Chia·Niran Abbas Ali·Adem Kilicman
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Abstract

We study extremal type problem arising from the question: What is the maximum number of edge-disjoint non-crossing perfect matchings on a set S of 2n points in the plane such that their union is a triangle-free geometric graph? We approach this problem by considering four different situations of S. In particular, in the general position, we obtain (i) a sufficient condition for the existence of n edge-disjoint non-crossing perfect matchings in the general position whose union is a maximal triangle-free geometric graph, and (ii) a lower bound on the number of edge-disjoint non-crossing perfect matchings whose union is a triangle free geometric graph.

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Hazim Michman Trao, Gek L. Chia, Niran Abbas Ali, Adem Kilicman. 2016-11-30. Non-Crossing Perfect Matchings and Triangle-Free Geometric Graphs. https://arxiv.org/abs/1611.10058

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