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 resultconstructively 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 10Maximum Cardinality 1-restricted Simple 2-matchings∗David HartvigsenUniversity of Notre DameNotre Dame, IN 46556-5646Hartvigsen.1@nd.eduSubmitted: ... follow. They characterize the maximum size of a 1-restricted 2-matching and the diﬀerence between the maximum sizes of a maximum 2-matching anda maximum 1-restricted 2-matching.the electronic journal...

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Báo cáo toán học: "Maximum subsets of (0, 1] with no solutions to x + y = kz" pptx

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Báo cáo toán học: "Maximum Degree Growth of the Iterated Line Graph" pdf

... Thefocus 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...

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Báo cáo toán học: "Maximum matchings in regular graphs of high girth" ppt

... some backgroundinformation. Let n(d, g) be the least number of vertices in a (d, g)-graph. The simplest lowerbound on n(d, g) is the Moore bound, which states that n(d, g) ≥ n0(d, g). It can ... adjacency matrix λ(G) is smallerthan d −  for some  = (d, g) > 0.The proof of Theorem 1 is a simple combination of the correct ingredients. One ingredientis the characterization of the matching...

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Báo cáo toán học: "Maximum Independent Sets in Certain Powers of Odd Cycles" doc

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

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Báo cáo toán học: "Maximum exponent of boolean circulant matrices with constant number of nonzero entries in their generating vector" docx

... matrix.Next, given n and r ∈ {2, . . . , n}, we determine the maximum order of bases for Znwith constant cardinality r. We also give subsets o f Znwith such an order. Since weare only interested in ... havethe same order as S.Let us denote by Sn,rthe set of bases for Znthat contain 0 and have cardinality r,with 2 ≤ r ≤ n. Note that for each pair (n, r), Sn,ris nonempty. Clearly, if n ... = h ∈ A.The next result is an immediate consequence of ii) in Lemma 2.2. We denote by |M|the cardinality of the set M.Corollary 2.3 Let A ⊆ Znbe nonempty. Then |H(A)| divides |A|.Next we...

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Báo cáo toán học: "Maximum Multiplicity of a Root of the Matching Polynomial of a Tree and Minimum Path Cover" pdf

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

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Báo cáo toán học: "Maximum Multiplicity of Matching Polynomial Roots and Minimum Path Cover in General Graphs" ppsx

... matching polynomial roots can be arbitrarily large.1 IntroductionAll the graphs in this paper are simple. The vertex set and edge set of a graph G aredenoted 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 polynomialare simple. The above is the source of motivation for our work. In this note, we give a necessaryand ... diﬃcult to see that we may assume a minimum-sized path cover of Gkal-ways contain P1. Then a simple induction yields minpc(Gk) = k. Next, we claim thatmaxmult(Gk) = 1. Let Ti= Pi\...

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Báo cáo toán học: "Unitary equivalence of restricted shifts " pdf

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Báo cáo toán học: "Systemes dinamiques generalises et corespondances " pdf

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