Báo cáo toán học: "THE INDEPENDENCE NUMBER OF DENSE GRAPHS WITH LARGE ODD GIRTH" ppsx

... Denley’s Theorem 4. References 1. Denley, T., The Independence number of graphs with large odd girth, The Electronic Journal of Combinatorics 1 (1994) #R9. 2 We can now prove the following theorem. Theorem ... is sharp for the regular complete bipartite graphs K aa . The above results are readily extended to graphs of larger odd girth. Lemma 2: Let G have odd girth 2...

Ngày tải lên: 07/08/2014, 06:20

... for the independence number of general graphs of a given odd girth. We shall prove some similar bounds to those we prove for regular graphs in terms of a measure of the concentration of edges. Monien ... prove our results for graphs of odd girth at least 7. Dealing with graphs with larger odd girth will simply require a generalisation of this argument. Theo...

Ngày tải lên: 07/08/2014, 06:20

... the number of partitions of (the number) n,andQis its ordinary generating function. Also, define p(n, k) to be the number of partitions of n with largest part at most k. We will have use of the ... values of n, we shall use elementary estimates and some well-known bounds for ordinary partitions (of a number) to express most values of b n in terms of the number of o...

Ngày tải lên: 07/08/2014, 06:20

... number be known as M k (n). I conjecture that this is in fact the minimum number of monotone subsequences of length k +1. the electronic journal of combinatorics 9(2) (2002), #R4 2 Table 3: Number ... extremal that with a little more effort the method can be adapted. Proof of Theorem 4 for n odd The canonical extremum from Section 1 is of this form, so M 2 (n) monotone subs...

Ngày tải lên: 07/08/2014, 07:21

... permutation of rows and columns A is a block diagonal matrix in which each block is a square all-1 matrix. Proof of Theorem 1.1: The square of the number of perfect matchings of G counts ordered pairs of ... spanning 2-regular subgraphs H  of G, where now we allow odd cycles and cycles of length 2 as well. Here, too, each such H  is counted 2 s times, where s is the num...

Ngày tải lên: 07/08/2014, 15:22

... crossing number of projective graphs with bounded degree. 1 Introduction We recall that the face–width of a graph G embedded in a surface Σ is the minimum number of intersections of G with a noncontractible ... and the crossing number of graphs with an excluded minor. New York J. Mathematics 13 (2007), 117–146. the electronic journal of combinatorics 15 (2008), #R4...

Ngày tải lên: 07/08/2014, 15:23

... T ∗ R is the set of hyperedges of T colored with red by c(x 1 , x 2 ). Consider the complete r −2-uniform hypergraph F ⊂ T ∗ spanned by the vertex set of e ∪f. Among all pairs of edges of F with distinct ... The chromatic number of Kneser hypergraphs, Trans- actions of the American Mathematical Society 298 (1986), pp. 359-370. [3] I. B´ar´any, A short proof of Kneser’s c...

Ngày tải lên: 07/08/2014, 21:20

... tight. The odd edge-connectivity of a graph G is the size of a smallest odd edge cut of G.The odd girth of G is the length of a shortest odd cycle of G. Zhang [19] proposed a strengthing of Jaeger’s ... no thread of length at least 2k. For otherwise, for any internal vertex x of a thread of length the electronic journal of combinatorics 8 (2001), #R25 3 Circular...

Ngày tải lên: 07/08/2014, 06:22

... investigate Laplacian spread of graphs , and prove that there exist exactly five types of tr icyclic graphs with maximum Laplacian spread among all tricyclic graphs of fixed order. 1 Introduction In ... vertices of the star, respectively [4]. A tricyclic graph is a connected graph in which the number of edges equals the number of vertices plus two. In this paper, we stud...

Ngày tải lên: 07/08/2014, 21:21

... Proofs of Auxiliary Lemmas 7.1 Proof of Lemma 2.2 The proof of Lemma 2.2 relies on the following general tail bound, which is a consequence of Azuma’s inequality (cf. [17, p. 38] for a proof). Lemma ... exp(− ¯ d min /(2C)), the electronic journal of combinatorics 16 (2009), #R138 44 The spectral gap of random graphs with given expected degrees ∗ Amin Coja-Oghlan University o...

Ngày tải lên: 08/08/2014, 01:20