Matchings with Prescribed Color Counts
Tudor Popescu
TL;DR
This paper proves a new result about perfect matchings in a bipartite graph with edges colored in red and blue, where each vertex has a prescribed number of edges of each color.
Contribution
It introduces a novel theorem regarding the existence of perfect matchings under specific coloring and degree constraints in bipartite graphs.
Findings
Existence of perfect matchings under prescribed color degree conditions
New combinatorial conditions for edge-colored bipartite graphs
Theoretical advancement in graph coloring and matching theory
Abstract
In this note, we prove an interesting result about perfect matchings in a complete bipartite graph with 2n vertices on each side, whose edges are colored in red and blue such that each vertex is part of n red edges and n blue edges.
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Taxonomy
TopicsFace and Expression Recognition