Minimum Cost Homomorphisms to Semicomplete Multipartite Digraphs
G. Gutin, A. Rafiey, A. Yeo

TL;DR
This paper extends the classification of the minimum cost homomorphism problem to semicomplete k-partite digraphs and bipartite tournaments, providing a comprehensive complexity analysis for these classes.
Contribution
It generalizes previous results by classifying the complexity of MinHOMP for semicomplete k-partite digraphs and bipartite tournaments.
Findings
Dichotomy classification for semicomplete k-partite digraphs
Complexity results for bipartite tournaments
Extension of previous classifications to broader graph classes
Abstract
For digraphs and , a mapping is a {\em homomorphism of to } if implies For a fixed directed or undirected graph and an input graph , the problem of verifying whether there exists a homomorphism of to has been studied in a large number of papers. We study an optimization version of this decision problem. Our optimization problem is motivated by a real-world problem in defence logistics and was introduced very recently by the authors and M. Tso. Suppose we are given a pair of digraphs and a positive integral cost for each and . The cost of a homomorphism of to is . Let be a fixed digraph. The minimum cost homomorphism problem for , MinHOMP(), is stated as follows: For input digraph and costs for each $u\in…
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Taxonomy
TopicsAdvanced Graph Theory Research · Limits and Structures in Graph Theory · graph theory and CDMA systems
