Geodesic
Extremal graphs for blow-ups of cycles and trees
Hong Liu1
1University of Illinois at Urbana-Champaign
The electronic journal of combinatorics, Tome 20 (2013) no. 1
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The blow-up of a graph H is the graph obtained from replacing each edge in H by a clique of the same size where the new vertices of the cliques are all different. Erdős et al. and Chen et al. determined the extremal number of blow-ups of stars. Glebov determined the extremal number and found all extremal graphs for blow-ups of paths. We determined the extremal number and found the extremal graphs for the blow-ups of cycles and a large class of trees, when n is sufficiently large. This generalizes their results. The additional aim of our note is to draw attention to a powerful tool, a classical decomposition theorem of Simonovits.
DOI : 10.37236/2856
Classification : 05C35, 05C38, 05C05, 05C70
Mots-clés : extremal graphs

Hong Liu  1

1 University of Illinois at Urbana-Champaign 
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Hong Liu. Extremal graphs for blow-ups of cycles and trees. The electronic journal of combinatorics, Tome 20 (2013) no. 1. doi: 10.37236/2856

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