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Two remarks on retracts of graph products

✍ Scribed by Sandi Klavžar

Publisher
Elsevier Science
Year
1992
Tongue
English
Weight
545 KB
Volume
109
Category
Article
ISSN
0012-365X

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✦ Synopsis

KlavZar, S., Two remarks on retracts of graph products, Discrete Mathematics 109 (1992) 155-160.

Let H be a bipartite graph and let G,, be the Mycielski graph with x(G) = n, n 3 4. Then the chromatic number of the strong product of G, by H is at most 2n -2. We use this result to show that there exist strong products of graphs in which a projection of a retract onto a factor is not a retract of the factor. We also show that in the Cartesian product of graphs G and H, any triangles of G transfer in H, whenever G and H are connected and G is stronglytriangulated, weakly-triangulated or four-cycle free.

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