On well quasi-order of graph classes under homomorphic image orderings

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In this paper we consider the question of well quasi-order for classes defined by a single obstruction within the classes of all graphs, digraphs and tournaments, under the homomorphic image ordering (in both its standard and strong forms). The homomorphic image ordering was introduced by the authors in a previous paper and corresponds to the existence of a surjective homomorphism between two structures. We obtain complete characterisations in all cases except for graphs under the strong ordering, where some open questions remain.
Original languageEnglish
Pages (from-to)164-175
Number of pages12
JournalEuropean Journal of Combinatorics
Early online date7 Apr 2017
Publication statusPublished - Jun 2017


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