Báo cáo toán học: "Densities of Minor-Closed Graph Families" potx

... number of reaches of G M equals the algebraic and geometric multiplicity of 0 as an eigenvalue of M. Proof. Let R 1 , , R k denote the reaches of G M and let H i denote the exclusive part of R i for ... 3 Proof. Let M = D − DS be given as stated. As in the proof of Theorem 3.2 above, we may assume without loss of generality that S ii = 1 whenever D ii =0. (2) We further observ...

Ngày tải lên: 07/08/2014, 13:21

... set of limiting densities of minor-closed graph families is the topological closure of the set of densities of density-minimal graphs. Proof. By Corollary 8, the set of limiting densities of minor-closed ... from? Planar graphs, forests, outerplanar graphs, and matchings all form instances of minor- closed families of simple graphs, families of the graphs with the pr...

Ngày tải lên: 08/08/2014, 12:22

... from any element of A i to an element of A i±1 and from any element of G i to an element of G i±1 , there is a break/repair path from any element of the B i ∪B i+1 to some element of (A 0 |G 0 ). ... number of 1’s is even, one has the same parity for the number of 1’s in the rest of the positions of v. the electronic journal of combinatorics 12 (2005), #R59 10 (b) there...

Ngày tải lên: 07/08/2014, 13:21

... Characterization of Irregular (λ, µ)-graphs In this section we prove that K 1 ∨ mK λ+1 is the only type of connected irregular (λ, µ)- graphs. A nice interpretation of the result is that if each pair of friends ... m(λ + 1) + 1. Proof. If µ = 0, then G has no pair of vertices with distance two apart. Thus each component of G is a complete graph. Since G is a (λ, µ) -graph, each c...

Ngày tải lên: 07/08/2014, 15:23

... presentation of K n , we define a class of fully coloured graphs called admissible graphs in definition 59. One of them, written Γ n , has the property that the underlying graph is the Cayley graph of (K n , ... confined to (2, 3)-graphs. Moreover, the natural proof of it is almost a tautology. We won’t need any of this. The rank of a fully coloured graph (V, S, m) is defined...

Ngày tải lên: 07/08/2014, 21:21

... squares of column −59 and row 59 of Q 119 are covered, so a copy of Q 118 is dominated. the electronic journal of combinatorics 8 (2001), #R29 16 Values of Domination Numbers of the Queen’s Graph Patric ... squares of these orthogonals are not covered by the required lines for a 0-cover D of size 2k + 1 for Q 4k+1 with e = f + 2; since the set of required lines of D is s...

Ngày tải lên: 07/08/2014, 06:22

... Constructions for cubic graphs of large girth. Electron. J. Combin., 5 (1998) A1. [2] M. J. Hoare, On the girth of trivalent Cayley graphs. Graphs and Other Combinatorial Topics (Proceedings of the Third ... semiregularly. According to [1], this graph is the smallest known trivalent graph of girth 14, improving the previous bound of 406 [2]. An electronic copy of the adjacency...

Ngày tải lên: 07/08/2014, 06:23

... Thenµ p (I) ≤ p. Our proof uses measure preserving homomorphisms between graphs. One of the fundamental questions first studied in extremal graph theory is the question of bounding the size of an intersecting ... importance of being biased (1.36 hardness of approximating Vertex-Cover). Annals of Mathematics,toappear.Proc. of 34th STOC, 2002. [2] P. Erd˝os, C. Ko, R. Rado, Inter...

Ngày tải lên: 07/08/2014, 13:21

... block of either π 1 or π 2 must be in t he same block of π. Hence the blocks of π are the blocks of π 1 ∨ π 2 . Let B be a block of π and for i = 1, 2 let w i (B) denote the number of vertices of ... definitions of tree-decompositions and of tree-width. A tree-decomposition of a graph G = (V, E) is a pair  S = {S i |i ∈ I}, T = (I, F)  where S is a family of subsets...

Ngày tải lên: 07/08/2014, 21:21

... of the graph G. We also establish a link between an algebraic property of the rational function (the factorization of the numerator) and a combinatorial property of the graph (the existence of ... denominator of the reduced form of Ψ P is known (Bou07). In this article, the first author has investigated the effects of elementary transformations of the Hasse diagram of a...

Ngày tải lên: 08/08/2014, 01:20