Báo cáo toán học: "Large bounded degree trees in expanding graphs" pptx

... Finally, in Section 5, based on this study, we give very short proofs of our main results – Theorems 4, 5, 6 and 7. 2 Embedding trees in expanding graphs We start by defining a class of expanding ... almost spanning trees in random graphs, submitted. [4] J. Friedman and N. Pipp enger, Expanding graphs contain all small trees, Combinator- ica 7 (1 987), 71–76. [5] P. Haxell, Tr...

Ngày tải lên: 08/08/2014, 11:20

... 05D15 Keywords: Packing trees, matchings in hypergraphs Abstract Let T be a tree with t vertices. Clearly, an n vertex graph contains at most n/t vertex disjoint trees isomorphic to T . In this paper ... there are d ways to allocate x t−1 in G. Suppose that R i ,1≤ i<t− 1, is already allocated in G,andy i is allocated in a vertex v i in G.Sincev i is of degree d in G and...

Ngày tải lên: 07/08/2014, 06:22

... are listed in Table 10, with λ vy = c in the top 11 lines and λ vy = e in the remainder. Note that λ v /∈ {a, b, λ vy }, since otherwise |Λ(y)|  3. So, using a to denote ‘anything in {a, b, c, ... sepachain; and if G 1 and G 2 are sepachains then the graphs formed by joining them in series and in parallel, as in Figs 1(b) and 1(d), are both sepachains. A sepachain is nontrivial...

Ngày tải lên: 07/08/2014, 13:21

... deter- mining number of a graph G is the smallest integer r so that G has a determining set of size r. Boutin introduced determining in [5]. Both distinguishing labelings and determining sets illuminate ... the subgraph of G induced by S. A d- distinguishing labeling for H as a graph induces a d-distinguishing labeling for S as a subset of V (G). Proof. Find a d-distinguishing labeling for...

Ngày tải lên: 07/08/2014, 15:22

... with distinct colors, color the rest of the graph with the remaining colors. Let S induce a rainbow copy of H in G in this coloring. Suppose v ∈ S. Since k − 1 non-neighbors of v must be in S, we ... vertices spanning C 4 in G. Color all vertices of U  with color 1 and rainbow color the remaining vertices with colors {2, . . . , k}. Under this coloring, there is a rainbow copy of H c...

Ngày tải lên: 07/08/2014, 15:22

... Proposition 2.5, the following result is obtained. Proposition 3.1. Let α 1 , α 2 be distinct elements in F q . Then a point P = (u : v : 1) belongs to a line joining two points of D H,α 1 ∪D H,α 2 provided ... plane coordinatized over the finite field with q elements F q , is a point-set whose secants cover P G(2, q), that is, any point of P G(2, q) belongs to a line joining two distinct poi...

Ngày tải lên: 07/08/2014, 15:23

... publication in Combinatorica. [12] M. Marciniszyn, R. Sp¨ohel, and A. Steger. Online Ramsey games in random graphs. Accepted for publication in Combinatorics, Probability and Computing. the electronic ... Theorem 1 In this section we prove our results for the edge case. We start by introducing the notion of r-matched graphs already mentioned in the introduction, and stating a result...

Ngày tải lên: 07/08/2014, 21:21

... Notice that v is unique since otherwise there is a cycle in M not contained in M. We conclude by joining R and γ v to obtain a new weakly decreasing ray R ′ starting at a vertex in M which is cofinal ... of t hem are in nite trees, every single one of them having a unique weakly decreasing ray. So, the number of non cofinal weakly decreasing rays is in nite and then not only the inequa...

Ngày tải lên: 07/08/2014, 21:21

... cycle H in D is a Hamilton cycle in the graph underlying D such that all pairs of consecutive arcs in H form a directed path in D. An anti-directed Hamilton cycle H in D is a Hamilton cycle in the ... out of v (respectively, directed into v). Let δ 0 (D) = min v∈V (D) {min{d + (v, D), d − (v, D)}}. The graph underlying D is the graph obtained from D by ignoring the directions of t...

Ngày tải lên: 08/08/2014, 01:20

Ngày tải lên: 05/08/2014, 15:20