A Note on Randomly Colored Matchings in Random Bipartite Graphs

Alan Frieze ()
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Alan Frieze: Carnegie Mellon University

A chapter in Discrete Mathematics and Applications, 2020, pp 199-205 from Springer

Abstract: Abstract We are given a bipartite graph that contains at least one perfect matching and where each edge is colored from a set Q = c 1 , c 2 , … , c q $$Q=\left \{c_1,c_2,\ldots ,c_q\right \}$$ . Let Q i = e ∈ E ( G ) : c ( e ) = c i $$Q_i=\left \{e\in E(G):c(e)=c_i\right \}$$ , where c(e) denotes the color of e. The perfect matching color profile mcp(G) is defined to be the set of vectors (m 1, m 2, …, m q) ∈ [n]q such that there exists a perfect matching M such that |M ∩ Q i| = m i. We give bounds on the matching color profile for a randomly colored random bipartite graph.

Date: 2020
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DOI: 10.1007/978-3-030-55857-4_8

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