Báo cáo toán học: "The independence number of graphs with large odd girth" ppt

... 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

... 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

... 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...

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