منابع مشابه
Absolute retracts of split graphs
It is proved that a split graph is an absolute retract of split graphs if and only if a partition of its vertex set into a stable set and a complete set is unique or it is a complete split graph. Three equivalent conditions for a split graph to be an absolute retract of the class of all graphs are given. It is finally shown that a reflexive split graph G is an absolute retract of reflexive spli...
متن کاملRetracts of Products of Chordal Graphs
In this article, we characterize the graphs G that are the retracts of Cartesian products of chordal graphs. We show that they are exactly the weakly modular graphs that do not contain K2,3, the 4-wheel minus one spoke W − 4 , and the k-wheels Wk (for k ≥ 4) as induced subgraphs. We also show that these graphs G are exactly the cage-amalgamation graphs as introduced by Brešar and Tepeh Horvat (...
متن کاملRetracts of strong products of graphs
Let G and H be connected graphs and let G ∗ H be the strong product of G by H. We show that every retract R of G ∗ H is of the form R = G′ ∗ H ′, where G′ is a subgraph of G and H ′ one of H. For triangle–free graphs G and H both G′ and H ′ are retracts of G and H, respectively. Furthermore, a product of finitely many finite, triangle–free graphs is retract–rigid if and only if all factors are ...
متن کاملHedetniemi's Conjecture and the Retracts of a Product of Graphs
We show that every core graph with a primitive automorphism group has the property that whenever it is a retract of a product of connected graphs, it is a retract of a factor. The example of Kneser graphs shows that the hypothesis that the factors are connected is essential. In the case of complete graphs, our result has already been shown in [4, 17], and it is an instance where Hedetniemi’s co...
متن کاملThe competition numbers of ternary Hamming graphs
The competition graph of a digraph D is a graph which has the same vertex set as D and has an edge between x and y if and only if there exists a vertex v in D such that (x, v) and (y, v) are arcs of D. For any graph G, G together with sufficiently many isolated vertices is the competition graph of some acyclic digraph. The competition number k(G) of a graph G is defined to be the smallest numbe...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1992
ISSN: 0012-365X
DOI: 10.1016/0012-365x(92)90054-j