Báo cáo toán học: "Graph Theory for Metric Dimension and Diameter" docx

... cardinality is a metric basis of G, and |S| is the metric dimension of G, denoted by β(G). For positive integers β and D, let G β,D be the class of connected graphs with metric dimension β and diameter ... 20 Extremal Graph Theory for Metric Dimension and Diameter ∗ Carmen Hernando † Departament de Matem`atica Aplicada I Universitat Polit`ecnica de Catalunya Barcel...

Ngày tải lên: 08/08/2014, 12:22

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Ngày tải lên: 05/08/2014, 09:46

... 0 and t − 1 exactly once for each e t ≤ i and lb t takes on each value between 1 and t − 1 exactly once for each e t >i. We list the values of r t in increasing order first for e t =0,nextfore t = ... K. Briggs and J. B. Remmel, A rook theory model for the p, q-analogues of Hsu and Shuiue’s Generalized Stirling Numbers, in preparation. [9] M. Dworkin, An interpretation...

Ngày tải lên: 07/08/2014, 08:22

... of a standard tableaux T λ of shape λ and vacillating tableaux P λ of shape λ and length 2k for some λ ∈ Λ k n . Our bijection uses jeu de taquin and RSK column insertion. If T is a standard ... Dulucq and Sagan [DS] extend this insertion to work for partial matchings (and other generalizations for skew oscillating tableaux) and Roby [Ry2] shows that the growth diagrams also...

Ngày tải lên: 07/08/2014, 08:22

... x j = 0 for some j ∈ {1, 2, . . . , t}. Let a k = |V k |, a j = |V j | and  = x k a j a k /(a j + a k ). Define a new weighting x  by x  v = x v for v ∈ V \(V k ∪ V j ), x  v = /a j for v ... x v for v ∈ V \(V k ∪ V j ), x  v = /a j for v ∈ V j and x  v = x k − /a k for v ∈ V k . It is straightforward to check that x  ∈ S p and λ(G, x  ) > λ(G, x), co...

Ngày tải lên: 07/08/2014, 15:23

... notation, the basic Random graph model and statement of the result for Random gra phs. In Section 3 we present two proofs. Section 4 shows that out bound is tight for quasi-random graphs. In Section ... Lemmas 10 and 11, respec- tively. For these lemmas, we assume v(1) = v min = b > 0 and define S t and n t analogously: • S 1 = {1} • S t+1 = {i : i ∈ N(S t ) and v(i)  b(1 +...

Ngày tải lên: 08/08/2014, 01:20

... minimum discrepancy problem by giving an explicit for- mula in terms of R and S for it. On the other hand, the problem of finding an explicit formula for the maximum discrepancy turns out to be very ... the following: 1. Region i is connected for each i =1, 2, and 2. The intersection of each row of A with region i is connected for each i =1, 2, and define, for each A ∈A(R, S),...

Ngày tải lên: 07/08/2014, 06:20