Non-Crossing Perfect Matchings and Triangle-Free Geometric Graphs
Combinatorics
2017-09-14 v2
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.
Keywords
Cite
@article{arxiv.1611.10058,
title = {Non-Crossing Perfect Matchings and Triangle-Free Geometric Graphs},
author = {Hazim Michman Trao and Gek L. Chia and Niran Abbas Ali and Adem Kilicman},
journal= {arXiv preprint arXiv:1611.10058},
year = {2017}
}
Comments
18 pages, 4 figures