Báo cáo toán học: "Graph Powers and Graph Homomorphism" ppsx

Ngày tải lên: 05/08/2014, 09:46

... by d G (x) the degree of x in a graph G and by G[X] the subgraph of G induced by a set of vertices X. The classic Brooks’ theorem states that any simple connected graph G with maximum degree ∆ ... is a complete graph, or an odd cycle; moreover, |V (B)|≥3. If B = G 2 there must be an edge between V (B)andP 1 since G is connected, if B = G 2 there is an edge between V (B) and P 1 sinc...

Ngày tải lên: 07/08/2014, 07:21

... one-factorizations F = {F 0 , ,F 2n−2 } and G = {G 0 , ,G 2m−2 } of K 2n and K 2m on the points X and Y , respectively, it is easy to see that FG =  F i G j : i =0, ,2n − 2andj =0, ,2m − 2    F ∗ i : ... NSERC post-doctoral fellowship. References [1] L.D. Andersen. Factorizations of graphs. In The CRC Handbook of Combinatorial Designs, C.J. Colbourn and J.H. Dinitz, eds., CRC Pres...

Ngày tải lên: 07/08/2014, 08:22

... Petersen graph any two vertices u and v. Such a graph must be matching covered and, moreover, cannot be bipartite if it has more than two vertices. A 3-connected bicritical graph is a brick. Any graph ... covered graph. The second argument constructs S in those matching covered graphs in which it exists. We now present the relevant definitions, notation and background. The vertex...

Ngày tải lên: 07/08/2014, 15:22

... vertices {a} and {b} to get the second graph. The third graph is obtained by unifying {c} and {d} in the second graph, while the last graph is obtained from the third graph by unifying {a, b} and {c, ... quartet graph of Q, denoted G Q , as follows. The vertex set of G Q is the set of singletons of X and, for each q = ab|cd ∈ Q, there is an edge joining {a} and {b}, and a...

Ngày tải lên: 07/08/2014, 21:20

... N. Biggs, 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 ... we choose a set of unordered vertex pairs, (u, v), and for each σ ∈Gwe add the edge (σ ∗ (u),σ ∗ (v)) to the graph. To construct the required graph, we use the following 12 vertex pair...

Ngày tải lên: 07/08/2014, 06:23

... another. The non-crossing graph NC n is the graph whose vertex set is the set of nonempty subsets of [n]={1, ,n}, and whose edge set is {XY : X, Y are non-crossing}. The subgraph of NC n induced ... chromatic number, independence number, clique number and clique cover number of this graph are presented. For the chromatic number of this graph we show: n(log e n − Θ(1)) ≤ χ(NC n ) ≤...

Ngày tải lên: 07/08/2014, 13:21

... i and there is no j such that R(i) ⊂R(j) (properly). Since our graphs all have finite vertex sets, such maximal sets exist and are uniquely determined by the graph. For each reach R i of a graph, ... Q. 4.2 Corollary. Let G denote a directed graph and let L denote the Kirchhoff matrix L = D − Q. Suppose G has N vertices and k reaches. Then the algebraic and geometric multiplicity...

Ngày tải lên: 07/08/2014, 13:21

... polynomial upper bounds on π and σ in terms of the treewidth and maximum degree of a graph. Theorem 3.3. Every graph G with treewidth k and maximum degree ∆ ≥ 1 satisfies π(G) ≤ ck∆ and σ(G) ≤ ck∆ 3 for ... Guoli Ding and Bogdan Oporowski. Some results on tree decomposition of graphs. J. Graph Theory, 20(4):481–499, 1995. [15] Vida Dujmovi ´ c, Pat Morin, and David R. Wood. L...

Ngày tải lên: 07/08/2014, 21:20

... Anusch Taraz, and Andreas W ¨ urfl. Bandwidth, treewidth, separators, expansion, and universality. In Proc. Topological and Geometric Graph Theory (TGGT ’08). 2008. [10] Fred Buckley and Frank Harary. ... A graph G is obtained by pasting subgraphs G 1 and G 2 on a cut-vertex v of G if G = G 1 ∪ G 2 and V (G 1 ) ∩ V (G 2 ) = {v}. Lemma 5. Let G be the graph obtained by pastin...

Ngày tải lên: 07/08/2014, 21:20