Recolouring Homomorphisms to triangle-free reflexive graphs
Jae-baek Lee, Jonathan A. Noel, Mark Siggers

TL;DR
This paper proves that recoloring and reconfiguration problems for homomorphisms to triangle-free reflexive graphs can be solved efficiently in polynomial time, expanding understanding of graph homomorphism reconfiguration.
Contribution
It establishes polynomial-time algorithms for recoloring and reconfiguration problems specifically for triangle-free reflexive graphs, a previously unresolved case.
Findings
Recoloring problem is polynomial-time solvable for these graphs.
Reconfiguration problem can be decided efficiently in the same setting.
Results extend the class of graphs with known efficient reconfiguration algorithms.
Abstract
For a graph , the -recolouring problem asks, for two given homomorphisms from a given graph to , if one can get between them by a sequence of homomorphisms of to in which consecutive homomorphisms differ on only one vertex. We show that, if and are reflexive and is triangle-free, then this problem can be solved in polynomial time. This shows, at the same time, that the closely related -reconfiguration problem of deciding whether two given homomorphisms from a given graph to are in the same component of the Hom-graph , can be solved in polynomial time for triangle-free reflexive graphs .
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Taxonomy
TopicsAdvanced Graph Theory Research · Nanocluster Synthesis and Applications · Interconnection Networks and Systems
