Báo cáo toán học: "New results about set colorings of graphs" ppt

... shows a strong 3 -set coloring of BT 3 . 4 5 2 3 6 7 4 7 6 5 3 2 1 Figure 8: 3 -set coloring of BT 3 Figures 9 and 10 illustrate the strong set coloring scheme detailed in the proof of Theorem 1. ... finite sets of positive integers. The color of a n edge (u, v) is given by the symmetric difference of the colors of u and v. A g r aph is said to be set colorable if there exis...

Ngày tải lên: 08/08/2014, 12:23

... hypergraph H = (V, E) consists of a finite non-empty set V of vertices and a family E of edges which are non-empty subsets of V of cardinality at least 2. An edge e of cardinality r(e) is called ... u, v ∈ X. The λ -colorings of H for which (i) holds are also λ -colorings of H+X = (V, E+X) where E+X = E ∪ X \ E X where E X = {e ∈ E | X ⊂ e}, and vice versa. The λ -colorings...

Ngày tải lên: 08/08/2014, 01:20

... consider that the starting point of a Dyck path is the origin of a pair of axes; (see Fig. 1). The set of Dyck paths of semilength n is denoted by D n , and we set D =  n≥0 D n , where D 0 = ... the g enerating function A p (resp. B s ) of the set of all Dyck paths having prefix p (resp. suffix s), as well as the generating function Γ p,s of the set of all Dyck paths h...

Ngày tải lên: 08/08/2014, 14:23

... B(G). A biclique cover of a graph G is a collection B of bicliques K(X i ,Y i ), 1 ≤ i ≤ k,ofG whoseedgesetscovertheedgesetofG. That is, each edge of G is in at least one of the bicliques in B.Thebiclique ... bc(G), of a graph G is the minimum number of bicliques in a biclique cover of G.Abiclique partition of a graph G is a collection B of bicliques K(X i ,Y i ), 1 ≤ i ≤ k,...

Ngày tải lên: 07/08/2014, 13:21

... permutation action on a set Ω is a subset of Ω such that the only permutation of Ω that fixes every element in the subset is the identity. [11] Every graph has a determining set, since any set containing ... consists of all of the  n k  k-element subsets of [n] = {1, 2, . . . n}, and uv ∈ E(K n:k ) when the subsets corresponding to u and v have empty intersection. It is well k...

Ngày tải lên: 07/08/2014, 15:22

... is a subgraph of a self-complementary graph H of order n = 4(p +q), such that a self-complementary permutation of H has q +1 cycles, q of which having length four. Proof. The proof is by induction ... (edge-disjoint) placement (or packing) of two copies of G (of order n) into the complete graph K n . It is evident that subgraphs of self-complementary graphs of the same order...

Ngày tải lên: 07/08/2014, 15:23

... n, provided that T has at least λn leaves. 3 Expanding properties of random graphs For two not necessarily disjoint subsets of the set of vertices of a graph G, let e(A, B) :=    (a, b) ∈ A × B : {a, ... surely G(n, c/n) does not contain a pair of disjoint sets B and C of sizes at least βn and at least (1 −γ)n respectively with e(B, C) = 0. Proof. As in the proof of Lemma 1...

Ngày tải lên: 08/08/2014, 11:20

... defined as follows. the electronic journal of combinatorics 17 (2010), #R23 1 Definition 1. Let us consider a set V = [n] of n vertices and a set W = [m] of m elements. Define m = ⌊βn α ⌋ with α, ... istributions of these weights, the degree of a vertex is shown to depend on the weight of that particular vertex and on the distribution of the weights of the other vertex type....

Ngày tải lên: 08/08/2014, 11:20

... A generalization of the Gallai-Roy theorem, Graphs and Combinatorics 17 (2001) 681-685. [6] C. Lin, Simple proofs of results on paths representing all colors in proper vertex- colorings, Graph ... v) is called an ancestor of u. By Theorem 6.6 of [2], in every DFS tree if w and w ′ are adjacent, then one of them is a ncestor of another. In a graph G, a k-coloring of G is a fun...

Ngày tải lên: 08/08/2014, 12:23

... exist 1. a number r ∈ (0, 1); 2. a sequence of complex numbers z n , |z n | < r; Further results of the estimate of growth of entire solutions of some classes of algebraic differential equations Qi ... full text (HTML) versions will be made available soon. Further results of the estimate of growth of entire solutions of some classes of algebraic differential equati...

Ngày tải lên: 20/06/2014, 20:20