{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article7758","name":"Homomorphism Reconfiguration via Homotopy","abstract":"We consider the following problem for a fixed graph H: given a graph G and two H-colorings of G, i.e. homomorphisms from G to H, can one be transformed into the other by changing one color at a time, maintaining an H-coloring throughout.This is the same as finding a path in the Hom(G,H) complex. For H=K_k this is the problem of finding paths between k-colorings, which was recently shown to be in P for k\\leq 3 and PSPACE-complete otherwise (Bonsma and Cereceda 2009, Cereceda et al. 2011).\r\nWe generalize the positive side of this dichotomy by providing an algorithm that solves the problem in polynomial time for any H with no C_4 subgraph. This gives a large class of constraints for which finding solutions to the Constraint Satisfaction Problem is NP-complete, but paths in the solution space can be found in polynomial time.\r\n \r\nThe algorithm uses a characterization of possible reconfiguration sequences (that is, paths in Hom(G,H)), whose main part is a purely topological condition described in terms of the fundamental groupoid of H seen as a topological space.","keywords":["reconfiguration","recoloring","homomorphisms","homotopy","hom complex"],"author":{"@type":"Person","name":"Wrochna, Marcin","givenName":"Marcin","familyName":"Wrochna"},"position":59,"pageStart":730,"pageEnd":742,"dateCreated":"2015-02-26","datePublished":"2015-02-26","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/legalcode","copyrightHolder":{"@type":"Person","name":"Wrochna, Marcin","givenName":"Marcin","familyName":"Wrochna"},"copyrightYear":"2015","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.STACS.2015.730","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume6233","volumeNumber":30,"name":"32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)","dateCreated":"2015-02-26","datePublished":"2015-02-26","editor":[{"@type":"Person","name":"Mayr, Ernst W.","givenName":"Ernst W.","familyName":"Mayr"},{"@type":"Person","name":"Ollinger, Nicolas","givenName":"Nicolas","familyName":"Ollinger"}],"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article7758","isPartOf":{"@type":"Periodical","@id":"#series116","name":"Leibniz International Proceedings in Informatics","issn":"1868-8969","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume6233"}}}