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On embedding well-separable graphs. (English) Zbl 1157.05032
This paper is about guaranteeing that a given graph $H$ is a subgraph of an arbitrary graph $G$. The author considers graphs $H$ that are “far from being an expander”, namely $H$ is well-separable if there is a subset $S \subset V(H)$ of size $o(n)$ such that all components of $H-S$ are of size $o(n)$. Let $\Delta$ denote the maximum degree of $H$ and $\chi$ its chromatic number. The author shows that if $H$ is well-seperable, then for every $\Delta$ and $\gamma > 0$ there exists an $n_0$ such that if $G$ is of order $n \ge n_0$ and minimum degree $\delta(G) \ge (1 - 1/(2(\chi -1)) + \gamma)n$, one gets $H \subset G$. This work can be considered as a generalization of Turán’s Theorem, as well of a generalization of work by Erdös-Stone-Simonovits.
05C35Extremal problems (graph theory)
05C10Topological graph theory
Full Text: DOI
[1] S. Abbasi, Spanning subgraphs of dense graphs, Ph.D. Theses, Department of Computer Science, Rutgers, the State University of New Jersey, 1998.
[2] Alon, N.; Yuster, R.: Almost H-factors in dense graphs, Graphs combin. 8, 95-102 (1992) · Zbl 0769.05072 · doi:10.1007/BF02350627
[3] Alon, N.; Yuster, R.: H-factors in dense graphs, J. combin. Theory ser. B 66, 269-282 (1996) · Zbl 0855.05085 · doi:10.1006/jctb.1996.0020
[4] Bollobás, B.: Extremal graph theory, (1978) · Zbl 1099.05044
[5] Csaba, B.: On the bollobás -- eldridge conjecture for bipartite graphs, Comb. probab. Comput. 16, 661-691 (2007) · Zbl 1136.05029 · doi:10.1017/S0963548307008395
[6] Erdős, P.; Simonovits, M.: A limit theorem in graph theory, Studia sci. Math. hungar. 1, 51-57 (1966) · Zbl 0178.27301
[7] Erdős, P.; Stone, A. H.: On the structure of linear graphs, Bull. amer. Math. soc. 52, 1089-1091 (1946) · Zbl 0063.01277 · doi:10.1090/S0002-9904-1946-08715-7
[8] Hajnal, A.; Szemerédi, E.: Proof of a conjecture of erd\h{o}s, Combinatorial theory and its applications, II, colloquia Mathematica societatis jános bolyai (1970)
[9] Komlós, J.: The blow-up lemma (survey), Combin. probab. Comput. 8, 161-176 (1999) · Zbl 0927.05041 · doi:10.1017/S0963548398003502
[10] Komlós, J.; Sárközy, G. N.; Szemerédi, E.: Proof of a packing conjecture of bollobás, Combin. probab. Comput. 4, 241-255 (1995) · Zbl 0842.05072 · doi:10.1017/S0963548300001620
[11] Komlós, J.; Sárközy, G. N.; Szemerédi, E.: Blow-up lemma, Combinatorica 17, 109-123 (1997) · Zbl 0880.05049
[12] Komlós, J.; Sárközy, G. N.; Szemerédi, E.: An algorithmic version of the blow-up lemma, Random struct. Algorithms 12, 297-312 (1998) · Zbl 0917.05071 · doi:10.1002/(SICI)1098-2418(199805)12:3<297::AID-RSA5>3.0.CO;2-Q
[13] Komlós, J.; Sárközy, G. N.; Szemerédi, E.: Proof of the Alon -- yuster conjecture, Discrete math., 255-269 (2001) · Zbl 0977.05106 · doi:10.1016/S0012-365X(00)00279-X
[14] Komlós, J.; Sárközy, G. N.; Szemerédi, E.: Spanning trees in dense graphs, Combin. probab. Comput., 397-416 (2001) · Zbl 0998.05012 · doi:10.1017/S0963548301004849
[15] J. Komlós, M. Simonovits, Szemerédi’s Regularity Lemma and its Applications in Graph Theory (survey), Combinatorics Paul Erdős is Eighty, vol. 2, Keszthely, 1993, pp. 295 -- 352. · Zbl 0851.05065
[16] E. Szemerédi, Regular partitions of graphs, Colloques Internationaux C.N.R.S No. 260 --- Problèmes Combinatoires et Théorie des Graphes, Orsay, 1976, pp. 399 -- 401. · Zbl 0413.05055
[17] Turán, P.: On an extremal problem in graph theory, Mat. fiz. Lapok 48, 436-452 (1941)