Báo cáo toán học: "Constrained graph processes" ppsx

... p) of graphs on a fixed vertex set V .In this context an up-set (down-set) is just a monotone increasing (decreasing) property of graphs on V .Note that we shall not distinguish sets A of graphs ... set of graphs S on V such that xy /∈ S and S ∪{xy} is isomorphic to H.LetU H (G p ,x,y) be the union of all subgraphs S of G p with S ∈H(x, y), and let X H (G p ,x,y)bethe number of such subgraphs...

Ngày tải lên: 07/08/2014, 06:20

Ngày tải lên: 05/08/2014, 15:21

... the same class. In general, a poset realizes two graphs simultaneously: one is its upper bound graph and another, its lower bound graph. These graphs may be thought of as two meanings of the poset, ... characterization of upper bound graphs, Congr. Numer. 40 (1983), 189–193. [6] J. R. Lundgren, J. S. Maybee, and F. R. McMorris, Two -graph inversion of competition graphs and upper bound gr...

Ngày tải lên: 07/08/2014, 06:20

... determining set if and only if every vertex in the graph can be uniquely identified by its own graph properties and its relationship to the vertices in S. Every graph has a determining set. Trivially the ... disjointness and nondisjointness; thus they induce graph automorphisms of K n:k . The Erd˝os-Ko-Rado Theorem shows that all automorphisms of Kneser graphs arise in this way [5]. Th...

Ngày tải lên: 07/08/2014, 13:21

... associated digraph does not have any dir ected cycles of even length. Any m × n matrix containing an n × n sub-matrix with either of these forms will have full rank. We translate this idea into a graph- theoretic ... matrix is small enough, and by a simple algorithm which has nothing to do with directed graphs, but the graph method may be more suitable for proving full rank if there is no...

Ngày tải lên: 07/08/2014, 21:21

... c? 1. Random graphs with prescribed structure. We can generate interesting classes of random graphs with prescribed structure. For example, let us consider H-free subgraphs of a fixed graph G. Let ... Proof of Theorem 2.10 A digraph is a set of edges (i, j) and these can equally well be viewed as the set of edges of a bipartite graph. So we consider there to be a digraph view and a bipartit...

Ngày tải lên: 08/08/2014, 12:22

... exact graphs strictly contains the clas s of compact graphs. More precisely: 1. If G i s a compact graph, then G is also exact. 2. Let G 1 , . . . , G m be k-regular conn ected compact graphs, ... cubic graph is exponential on krawczyk’s graphs, Discrete Math. 235 (20 01), no. 1-3, 69–77, Combinatorics (Prague, 1998). [7] P.J. Cameron, Automorphisms of graphs, Topics in Algebraic Graph ....

Ngày tải lên: 08/08/2014, 12:22

... r-uniform hypergraph has a p-equitable orienta- tion. Proof. Let H be an r-uniform hypergraph. Let X be the family of p-sets in V (H), and let Y = E(H). Let B be the bipartite graph with partite ... every graph has an equitable orientation is just the statement that every 2-uniform hypergraph has a 1-equitable o r ientation. We present three results about p-equitable orientations o f hype...

Ngày tải lên: 08/08/2014, 14:23

... distance-transitive, graph. This graph has intersection array { 110 , 81 , 12; 1 , 18 , 90 } ,and automorphism group M 22 :2. In [1], Brouwer, Cohen and Neumaier discuss many distance-regular graphs related ... representation has rank 6, with subdegrees 1, 55, 55, 66, 165, 330. Let Γ be the graph obtained by the edge-union of the orbital graphs corresponding to the two suborbits of lengt...

Ngày tải lên: 07/08/2014, 06:20

... Tur´an Graph. Theorem 1.1 shows that this conjecture holds when H is a complete graph. The next conjecture states that the extremal graphs yielding t 2 (n, H) are also the ex- tremal graphs yielding ... unique extremal graph. the electronic journal of combinatorics 7 (2000), #R47 2 subgraphs. For a fixed graph H,lett p (n, H) denote the maximum value of e p (G) taken over all graphs wit...

Ngày tải lên: 07/08/2014, 06:20