Báo cáo toán học: "Maximum Cardinality 1-restricted Simple 2-matchings" pdf

... max- imum number of edges in a 1-restricted simple 2-matching. We prove this result constructively by presenting a polynomial time algorithm for finding a 1-restricted simple 2-matching with a maximum ... − T) − 2 ∗ |T |, the electronic journal of combinatorics 14 (2007), #R73 10 Maximum Cardinality 1-restricted Simple 2-matchings ∗ David Hartvigsen University of Notre Dame Notre...

Ngày tải lên: 07/08/2014, 15:23

Ngày tải lên: 07/08/2014, 06:20

... The focus of this paper is to present a proof of this conjecture. In the following work, only finite simple connected graphs with no loops are con- sidered. Note that the iterated line graph of a path

Ngày tải lên: 07/08/2014, 06:20

... some background information. Let n(d, g) be the least number of vertices in a (d, g)-graph. The simplest lower bound on n(d, g) is the Moore bound, which states that n(d, g) ≥ n 0 (d, g). It can ... adjacency matrix λ(G) is smaller than d −  for some  = (d, g) > 0. The proof of Theorem 1 is a simple combination of the correct ingredients. One ingredient is the characterization of the...

Ngày tải lên: 07/08/2014, 13:21

... [6]. The odd cycles on seven or more vertices and their complements are, in a certain sense, the simplest graphs for which the Shannon capacity is not known. This follows fro m the Strong Perfect ... sake of brevity, we do not define here) or the fractional vertex packing number α ∗ (G) and the simple fact α(G × H) ≤ α(G)α ∗ (H). The fractional vertex packing number of the graph G is the max...

Ngày tải lên: 07/08/2014, 21:21

... matrix. Next, given n and r ∈ {2, . . . , n}, we determine the maximum order of bases for Z n with constant cardinality r. We also give subsets o f Z n with such an order. Since we are only interested in ... have the same order as S. Let us denote by S n,r the set of bases for Z n that contain 0 and have cardinality r, with 2 ≤ r ≤ n. Note that for each pair (n, r), S n,r is nonempty. Cle...

Ngày tải lên: 07/08/2014, 21:21

... 12 Consequently, Theorem 1.2. If G has a Hamiltonian path, then all roots of its matching polynomial are simple. The above is the source of motivation for our work. It is natural to ask when does equality ... number of vertex disjoint paths needed to cover it. 1 Introduction All the graphs in this paper are simple. The vertex set and the edge set of a graph G are denoted by V (G) and E(G)...

Ngày tải lên: 07/08/2014, 21:21

... matching polynomial roots can be arbitrarily large. 1 Introduction All the graphs in this paper are simple. The vertex set and edge set of a graph G are denoted by V (G) and E(G) respectively. A matching ... G. Consequently, Theorem 1.2. If G has a Hamiltonian path, then all roots of its matching polynomial are simple. The above is the source of motivation for our work. In this note, we gi...

Ngày tải lên: 08/08/2014, 12:23

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