Two remarks on retracts of graph products
نویسنده
چکیده
Let H be a bipartite graph and let Gn be the Mycielski graph with χ(G) = n, n ≥ 4. Then the chromatic number of the strong product of Gn 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 strongly–triangulated, weakly–triangulated or four–cycle free.
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 109 شماره
صفحات -
تاریخ انتشار 1992