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 کاملCharacterizing subgraphs of Hamming graphs
Cartesian products of complete graphs are known as Hamming graphs. Using embeddings into Cartesian products of quotient graphs we characterize subgraphs, induced subgraphs, and isometric subgraphs of Hamming graphs. For instance, a graph G is an induced subgraph of a Hamming graph if and only if there exists a labeling of E(G) fulfilling the following two conditions: (i) incident edges receive ...
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...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1997
ISSN: 0095-8956
DOI: 10.1006/jctb.1997.1746