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A classification of reflexive graphs: The use of ”holes”. (English) Zbl 0618.05041

A reflexive graph is an undirected graph with a loop at every vertex. A subgraph H of G is a retract of G if there is an edge-preserving map f of V(G) to V(H) which maps every vertex of H to itself. A reflexive graph variety is a class C of reflexive graphs which contains all direct products of members of C and which contains all retracts of members of C. It is shown (among others) that the lattice (with respect to inclusion) of reflexive graph varieties contains an infinite chain.

MSC:

05C99 Graph theory
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