Báo cáo toán học: "The maximum number of perfect matchings in graphs with a given degree sequence" docx

... square all-1 matrix. Proof of Theorem 1.1: The square of the number of perfect matchings of G counts ordered pairs of such matchings. We claim that this is the number of spanning 2-regular subgraphs ... Cuckler and J. Kahn, Entropy bounds for perfect matchings and Hamiltonian cycles, to appear. [3] S. Friedland, An upper bound for the number of perfect matching...

Ngày tải lên: 07/08/2014, 15:22

... for graphs of odd girth at least 7. Dealing with graphs with larger odd girth will simply require a generalisation of this argument. Theorem 1 Let G be a graph of order n containing containing ... results of this paper are designed to deal with the case when the average degree of the graph is large. We shall prove that an r-regular graph without 3 and 5 cycles has an...

Ngày tải lên: 07/08/2014, 06:20

... ≥ √ n ¯ d2 as claimed. This improves Denley’s Theorems 1 and 2. It is sharp for the regular complete bipartite graphs K aa . The above results are readily extended to graphs of larger odd girth. Lemma ... 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 1. Suppose...

Ngày tải lên: 07/08/2014, 06:20

... Knopfmacher Department of Computational and Applied Mathematics University of Witwatersrand Johannesburg, South Africa e-mail: arnoldk@gauss.cam.wits.ac.za A. M. Odlyzko AT&T Labs - Research Florham Park, ... 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 ordinary partitions of k with...

Ngày tải lên: 07/08/2014, 06:20

... permutation. Var- ious operations were then applied to it: transposing a pair of values in the permutation; reversing the order of a block of values in the permutation; rotating a block of values ... extremal permutations with 0 and n − 1 adjacent are as described in Theorem 4, and all such permutations are extremal. Proof Without loss of generality, suppose a permut...

Ngày tải lên: 07/08/2014, 07:21

... Klein, Multiple-source shortest paths in planar graphs. In: SODA 2005, Pro- ceedings, SIAM (2005), 146–155. [10] B. Mohar, A linear time algorithm for embedding graphs in an arbitrary surface. SIAM ... 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...

Ngày tải lên: 07/08/2014, 15:23

... paper with a large number of open problems in this area. 1 Introduction A k-cap in AG(n, q) (a nen-space over F q ) is a subset X ⊂ AG(n, q)ofsizek,nothree of whose points are collinear. When a ... q) 10 points. A similar bound holds for the minimum size of a complete cap in AG(2,q) since we can obtain AG(2,q)fromPG(2,q) by removing a line at in nity. We can ask...

Ngày tải lên: 07/08/2014, 13:21

... nilpotent of class c or supersolvable of length c then G acts with distinguishing number at most c +1. As a corollary, we obtain that all metacyclic groups act with distinguishing number at most 3 since ... Collins in [2] as a property of graphs. More specifically, the distinguishing number of a graph M, denoted D(M), is the smallest number of colors admitting a...

Ngày tải lên: 07/08/2014, 13:21

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Ngày tải lên: 05/08/2014, 09:46

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Ngày tải lên: 05/08/2014, 10:20