
TL;DR
This thesis explores various matching problems in geometric graphs, including maximum, bottleneck, plane, and strong matchings, providing bounds and algorithms across different geometric graph families.
Contribution
It introduces new bounds and algorithms for multiple matching problems in diverse geometric graphs, advancing understanding of their combinatorial properties.
Findings
Established bounds for maximum matchings in geometric graphs
Developed algorithms for non-crossing and strong matchings
Identified tight bounds and areas for further refinement
Abstract
A geometric graph is a graph whose vertex set is a set of points in the plane and whose edge set contains straight-line segments. A matching in a graph is a subset of edges of the graph with no shared vertices. A matching is called perfect if it matches all the vertices of the underling graph. A geometric matching is a matching in a geometric graph. In this thesis, we study matching problems in various geometric graphs. Among the family of geometric graphs we look at complete graphs, complete bipartite graphs, complete multipartite graphs, Delaunay graphs, Gabriel graphs, and -graphs. The classical matching problem is to find a matching of maximum size in a given graph. We study this problem as well as some of its variants on geometric graphs. The bottleneck matching problem is to find a maximum matching that minimizes the length of the longest edge. The plane matching problem…
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Taxonomy
TopicsAdvanced Graph Theory Research · Computational Geometry and Mesh Generation · Complexity and Algorithms in Graphs
