Báo cáo toán học: "Colorful Paths in Vertex Coloring of Graphs" pps

... a k -coloring. For simplicity we denote a χ(G) -coloring of G by χ -coloring. For a coloring of graph G, we say path P of G is a rainbow path if all vertices of P have different colors. A v-rainbow ... 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-...

Ngày tải lên: 08/08/2014, 12:23

... a vertex in D. An arbitrary set A of vertices in a graph G dominates itself and the vertices at distance one from it. The domination number, γ(G), of a graph G is the minimum size of a dominating ... bound was proved in [2] by exploiting Reed’s techniques in [9] and examining some of the cases in Reed’s proof more carefully and adding a dis- charging argument. However, exp...

Ngày tải lên: 07/08/2014, 15:22

... t, no two of which sharing an edge, h as an s-colored t-matching contained in its union. In the case r = 2 the conjecture is that a set of t+1 disjoint t-matchings has a t-rainbow matching. This ... 1)-rainbow (k + 1)-matching, contradicting the maximality of k. the electronic journal of combinatorics 16 (2009), #R119 5 of the matrix). A partial transversal (or plainly transvers...

Ngày tải lên: 08/08/2014, 01:20

... Here we are interested in rainbow matchings. The study of rainbow matchings began with the following conjectures. Conjecture 1 (Ryser [5]) Every Latin square of odd order has a Latin transversal. Conjecture ... graph. A rainbow matching of G is a matching in which no two edges have the same color. Let δ denote the minimum degree of G. We show that if |V (G)| ≥ 8δ 5 , then G has a...

Ngày tải lên: 08/08/2014, 14:23

... ≤ k,ofG whoseedgesetscovertheedgesetofG. That is, each edge of G is in at least one of the bicliques in B.Thebiclique cover number, bc(G), of a graph G is the minimum number of bicliques in a ... edges e of G. Proof. It follows immediately from (2) and (4) that bc ∗ (G) ≤ bp ∗ (G) since a weighting v of the edges of G that satisfies the constraints of (2) also satisfies th...

Ngày tải lên: 07/08/2014, 13:21

... one of the parts of λ, or by inserting a part of size 1 into λ. We employ the methods they developed in order to study the same problem for the following poset, which is of interest because of ... underlying set is the same, but µ covers λ if µ can be obtained from λ by adding 1 to one of the parts of λ, or by inserting a part of size 1 at the left or at the right of λ. We...

Ngày tải lên: 07/08/2014, 08:22

... a vertex in Q k (x)containsk+1 vertices in Q k (x). A ball centered on some vertex in a Q k (y) such that d(y, x) = 1 contains exactly one vertex in Q k (x). We consider γ theminimumnumberofverticesofthecodewecanfindinaQ k (x). Let ... 05C69,05C70,94B60 Abstract We introduce and study a common generalization of 1-error binary perfect codes and perfect single error correcting co...

Ngày tải lên: 07/08/2014, 13:21

... minimal r-twin-free graph for the induced subgraph relationship. Indeed, we have: the electronic journal of combinatorics 15 (2008), #N17 5 An r-twin-free graph contains a path P 2r+1 as an induced ... vertices. Let V H be the vertex- set of H. There exists in H a vertex v t which is not a cutvertex; by minimality of H, the con- nected induced subgraph H[V H −v t ] of H must have...

Ngày tải lên: 07/08/2014, 15:22

... linear realizations to be perfect in view of possible proofs by induction, we think it appropriate to emphasize the following results. Proposition 4.7 There exist perfect linear realizations of ... the complete string of odd numbers. Moreover, since we will be using either a string of −2’s or a string of +2’s, we must make sure that, respectively, 2h + 3 is the maximum of the od...

Ngày tải lên: 08/08/2014, 12:22

Ngày tải lên: 05/08/2014, 09:46