Hell, Pavol; Rival, Ivan Absolute retracts and varieties of reflexible graphs. (English) Zbl 0627.05039 Can. J. Math. 39, No. 3, 544-567 (1987). Let H be a subgraph of G. The graph H is said to be a retract of G if there is an edge-preserving map f of G to H such that \(f(h)=h\) for each vertex h of H. A triple of H is a set of three vertices a, b, c of H together with three nonnegative integers i, j, k such that no vertex of H satisfies \(d_ H(h,a)\leq i\), \(d_ H(h,b)\leq j\), and \(d_ H(h,c)\leq k.\) The triple (a,b,c;i,j,k) of H is said to be separated in G if there is no vertex g of G satisfying \(d_ G(g,a)\leq i\), \(d_ G(g,b)\leq j\), \(d_ G(g,c)\leq k.\) The authors give a characterization (in terms of varieties) of each graph in which all triples of H are separated. Further results concern absolute retracts and the so-called finite separation property. Reviewer: J.Širáň Cited in 1 ReviewCited in 31 Documents MSC: 05C99 Graph theory Keywords:separated triples; variety of graphs; retract; edge-preserving map; absolute retracts; finite separation property PDFBibTeX XMLCite \textit{P. Hell} and \textit{I. Rival}, Can. J. Math. 39, No. 3, 544--567 (1987; Zbl 0627.05039) Full Text: DOI