Báo cáo toán học: "Weighted spanning trees on some self-similar graphs" pot

... Yang, Spanning Trees on the Sierpinski Gasket, J. Stat. Phys., 126, No. 3, (2007), 649–667. [7] D. D’Angeli, A. Donno and T. Nagnibeda, Partition functions of the Ising mo del on some self-similar ... functions of the spanning trees in the directional model and in the Schreier model, are different. 3 Spanning trees on the Schr eier graphs of the Hanoi Towers group In this...

Ngày tải lên: 08/08/2014, 12:23

... attention to simplicial complexes. For basic definitions and results about decision trees, see Section 1. Fundamental results about optimal decision trees appear in Section 2; see Section 4 for some ... not 2-connected graphs. We concentrate on element-decision trees and do not consider more general set-decision trees. An interesting question is whether set-decision trees may provi...

Ngày tải lên: 07/08/2014, 08:22

... proposition: Proposition 2.4. Let M be an infinite graph and let f be a discrete Morse function defined on M. Given a ray R in M, the following conditions are equivalent: (i) f is weakly decreasing on ... function defined on M is a function f : M −→ R such tha t, for any p-simplex σ ∈ M: (M1) At most one (p + 1)- simplex τ containing σ verifies f (τ) ≤ f (σ). (M2) At most one (p − 1)-simple...

Ngày tải lên: 07/08/2014, 21:21

... be converted to a linear-time algorithm, as follows. Let G be a graph. We say that a vertex v 1 ∈ V (G)isspecial if one of the following conditions holds: (a) the degree of v 1 is at most one, (b) ... 1999. Mathematical Subject Classification: 05C15. 1 Introduction List colorings are a generalization of usual colorings that recently attracted consider- able attention, cf. [1, 8, 9, 11]. Origin...

Ngày tải lên: 07/08/2014, 06:20

... the color degree condition has a heterochromatic path of length at least k, with only one exceptional graph K 4 for k = 3, one exceptional graph for k = 4 and three exceptional graphs for k =5,for which ... color degree condition has a heterochromatic path of length at least k, with only one exceptional graph K 4 for k = 3, one exceptional graph G 4 for k = 4 and three exceptional graphs G 5...

Ngày tải lên: 07/08/2014, 13:21

... we explore several necessary conditions for the existence of an IC-coloring of a graph G. Without mention otherwise, all graphs we consider in what follows are con- nected. For graph terms, we ... we have a contradiction and the proof is complete. the electronic journal of combinatorics 15 (2008), #R43 2 n ≥ 3, we have f 4 = 10 ≤ 3 · 2 4−2 − 2 4−(n+2) − 1. This is a contradiction to that ......

Ngày tải lên: 07/08/2014, 15:23

... Since none of them contain a repetition, we are done. Now suppose that P contains exactly one tag. Of course this tag must start in the first and finish in the second half of P = w · w, having something ... applying the substitutions 0 → 01 1 → 10 the electronic journal of combinatorics 16 (2009), #N15 2 4 Conclusion It is easy to see that if a graph contains P 4 – a path consisting of four ver...

Ngày tải lên: 07/08/2014, 21:21

... D contains an anti-directed Hamilton cycle. In Section 3 of this paper we turn our attention to (P, Q) vertex-oriented Hamilton cycles. In [1] the following theorem giving a sufficient condition ... G ′ contains a Hamilton cycle. Thus, if δ 0 (D)  3 4 n and |P | is even, then D trivially contains a (P, Q) vertex-oriented Hamilton cycle for any partition V (D) = P ∪ Q of V (D). In Section ... d...

Ngày tải lên: 08/08/2014, 01:20

... 8: Constructing a component isomorphic to C. Given one of our constructed graphs, there are at most |C|+1 components isomorphic to C, since we have deliberately constructed one and we may have ... a component isomorphic to H. We will now consider the amount of double-counting: Each of our constructed graphs will contain at most 4|H|−e(H)+1 components isomorphic to H (since there were none ......

Ngày tải lên: 08/08/2014, 11:20

... collection S of dominated vertices from an old collection S  , we use Theorem 2.2 whenever pos sible to reject solutions. Also a combination of Theorems 2.2 and 2.6 can be used to reject solutions. ... efficiently. Consider the situation when a new set S—if necessary, we first apply the mapping f to get a pair S, f (S) that fulfills s(S)  s(f(S))—is to be considered for inclusion in a collectio...

Ngày tải lên: 08/08/2014, 14:23