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Extremal graphs for edge blow-up of graphs.
- Source :
-
Journal of Combinatorial Theory - Series B . Jan2022, Vol. 152, p379-398. 20p. - Publication Year :
- 2022
-
Abstract
- Given a graph H and an integer p , the edge blow-up H p + 1 of H is the graph obtained from replacing each edge in H by a clique of order p + 1 where the new vertices of the cliques are all distinct. The Turán numbers for edge blow-up of matchings were first studied by ErdÅ‘s and Moon. In this paper, we determine the range of the Turán numbers for edge blow-up of all bipartite graphs and the exact Turán numbers for edge blow-up of all non-bipartite graphs. In addition, we characterize the extremal graphs for edge blow-up of all non-bipartite graphs. Our results also extend several known results, including the Turán numbers for edge blow-up of stars, paths and cycles. The method we used can also be applied to find a family of counter-examples to a conjecture posed by Keevash and Sudakov in 2004 concerning the maximum number of edges not contained in any monochromatic copy of H in a 2-edge-coloring of K n. [ABSTRACT FROM AUTHOR]
- Subjects :
- *RAMSEY numbers
*BIPARTITE graphs
*EDGES (Geometry)
Subjects
Details
- Language :
- English
- ISSN :
- 00958956
- Volume :
- 152
- Database :
- Academic Search Index
- Journal :
- Journal of Combinatorial Theory - Series B
- Publication Type :
- Academic Journal
- Accession number :
- 153599318
- Full Text :
- https://doi.org/10.1016/j.jctb.2021.10.006