论文信息 - Spanning Trees in Dense Graphs

Spanning Trees in Dense Graphs

In this paper we prove the following almost optimal theorem. For any δ > 0, there exist constants c and n0 such that, if n [ges ] n0, T is a tree of order n and maximum degree at most cn/log n, and G is a graph of order n and minimum degree at least (1/2 + δ)n, then T is a subgraph of G.

[1] János Komlós,et al. On the square of a Hamiltonian cycle in dense graphs , 1996, Random Struct. Algorithms.

[2] L. Lovász. Combinatorial problems and exercises , 1979 .

[3] E. Szemerédi. Regular Partitions of Graphs , 1975 .

[4] Béla Bollobás,et al. Packings of graphs and applications to computational complexity , 1978, J. Comb. Theory, Ser. B.

[5] Vojtech Rödl,et al. The Algorithmic Aspects of the Regularity Lemma , 1994, J. Algorithms.

[6] Joel H. Spencer,et al. Edge disjoint placement of graphs , 1978, J. Comb. Theory B.

[7] E. Szemerédi. On sets of integers containing k elements in arithmetic progression , 1975 .

[8] János Komlós,et al. Blow-up Lemma , 1997, Combinatorics, Probability and Computing.

[9] János Komlós,et al. Proof of the Alon-Yuster conjecture , 2001, Discret. Math..

[10] Y. Kohayakawa. Szemerédi's regularity lemma for sparse graphs , 1997 .

[11] Miklós Simonovits,et al. Szemerédi's Partition and Quasirandomness , 1991, Random Struct. Algorithms.

[12] C. V. Eynden,et al. A proof of a conjecture of Erdös , 1969 .

[13] János Komlós,et al. Proof of a Packing Conjecture of Bollobás , 1995, Combinatorics, Probability and Computing.

[14] Endre Szemerédi,et al. Proof of the Seymour conjecture for large graphs , 1998 .

[15] János Komlós,et al. An algorithmic version of the blow-up lemma , 1998, Random Struct. Algorithms.