Báo cáo toán học: "Double-critical graphs and complete minors" pps

... where p and q are coprime and resolves the BAC Conjecture when p and q are coprime and either p or q is even. For the special case of factorisations of balanced complete bipartite graphs K n,n and ... k.Ifn 3 =2andt k =5,thenwe are covered by Sublemma 4.3. If n 3 =1,n 2 ≥ 2andt k ≥ 6letu = 6and = (0 2)(1 4)(3 5) and apply Sublemma 4.1. If n 3 =1,n 2 = 1 or 2, and t k =5,letσ...

Ngày tải lên: 07/08/2014, 08:20

Ngày tải lên: 05/08/2014, 09:46

Ngày tải lên: 05/08/2014, 15:21

... K r minor, and this completes the proof. The relation between α 2k and α 2k+1 in Corollary 1.6 cannot be extended to α 2k+1 and α 2k+2 as shown by the following examples (which are all planar and hence ... number and the stability number, in “Graph theory (Cambridge, 1981),” pp. 71–73, North-Holland Math. Stud. 62, North- Holland, 1982. [2] W. Goddard, M. A. Henning, Domination in p...

Ngày tải lên: 07/08/2014, 07:21

... number and the chromatic number of the Kneser graphs and the Schrijver graphs are equal has received attention and has been studied in several papers [6, 12, 15, 17, 19, 22]. Johnson, Holroyd, and ... 2005. [25] G. Spencer and F.E. Su, Using topological methods to force maximal complete bipartite subgraphs of Kneser graphs, Manuscript 2005 . [26] C. Tardif, Multiplicative gr...

Ngày tải lên: 08/08/2014, 11:20

... by x 1 , . . . , x d in G if and only if there is a vertex colored by v and adjacent to vertices colored by x 1 , . . . , x d in G ′ , and • G ′ is connected if and only if G is. We construct ... symmetric and non-symmetric) in S X , and let N X be the multi-set of the non-symmetric twigs in T X . We define t he relation M on a set of twigs such that (N, c, c ′ )M(N ′ , d, d ′ ) if...

Ngày tải lên: 08/08/2014, 12:23

... 10 complete graphs. 2 Notation All graphs considered in this paper are simple and finite. We let n(G) and m(G) denote the order and size of a graph G, respectively. The path, the cycle and the complete ... subset A and B such that the induced graphs G[A] and G[B] are edge-empty and complete, respectively, and, thus, we have a contradiction by Proposition 5.1. Suppose...

Ngày tải lên: 08/08/2014, 12:22

... Crytogr.,toappear. [3] A. Blass and F. Harary, Properties of almost all graphs and complexes, J. Graph Theory 3 (1979), 225–240. [4] A. Blass, G. Exoo, and F. Harary, Paley graphs satisfy all first-order ... Erd˝os, and K. Vijayan, A property of random graphs, Ars Combin. 19 (1985), 287–294. [9] R. Fagin, Probabilities on finite models, J. Symbolic Logic 41 (1976), 50–58. [10] W. H...

Ngày tải lên: 07/08/2014, 06:22

... one-factorizations F = {F 0 , ,F 2n−2 } and G = {G 0 , ,G 2m−2 } of K 2n and K 2m on the points X and Y , respectively, it is easy to see that FG =  F i G j : i =0, ,2n − 2andj =0, ,2m − 2    F ∗ i : ... NSERC post-doctoral fellowship. References [1] L.D. Andersen. Factorizations of graphs. In The CRC Handbook of Combinatorial Designs, C.J. Colbourn and J.H. Dinitz, eds., CRC Pre...

Ngày tải lên: 07/08/2014, 08:22

... part by NSF Grants DMS 0100472 and ITR 0205061. References [1] F. Chung, Diameters and eigenvalues, J. of Amer. Math. Soc. 2 (1989), 187-196. [2] F. Chung, V. Faber and T. A. Manteuffel, An upper ... Laplacians and the Cheeger inequality for directed graphs, Annals of Combinatorics 9 (2005), 1-19. the electronic journal of combinatorics 13 (2006), #N4 6 Proof. We consider g with gΦ 1/...

Ngày tải lên: 07/08/2014, 13:21