Báo cáo toán học: "On-line list colouring of graphs" pot

... wins if and only if in the process of the game list colouring Bob first colours a vertex of C 4 . Lemma 5 Let L be a 2 -list- assignment of C 4 , other than the lists in Figure 4 and Fig- ure 5. ... process of the game list colouring a graph G is par- tially coloured. If all uncoloured vertices of G are safe then Alice wins. Now we will consider a game list colouring but...

Ngày tải lên: 07/08/2014, 15:22

... independence number of general graphs of a given odd girth. We shall prove some similar bounds to those we prove for regular graphs in terms of a measure of the concentration of edges. Monien and ... for the independence number in terms of the odd girth, but instead of the average degree of the graph we have to use another measure of the concentration of edges. 8 Reference...

Ngày tải lên: 07/08/2014, 06:20

... [γ(K m )+1,g A −1], none of the genera admits the genus embedding of any the electronic journal of combinatorics 9 (2002), #R38 25 construction of graph H IB (s, k, l) up through the selection of faces F 1 through ... l)) = 2l +3. Proof: The proof proceeds just as in the proof of Theorem 3.2. For Part (i), the only difference is that here for H IB (s, k, l) we have deleted one edge...

Ngày tải lên: 07/08/2014, 07:21

... similar to that of Theorem 2 in Section 2 of [2]. Its proof is identical to the proof of that theorem, and depends only on the following modification of Proposition 5 from the same section of that paper. Lemma ... insertions of any type provided only that they can be followed by further insertions leading to an element of L. The number of elements of L of length n is then j...

Ngày tải lên: 07/08/2014, 13:21

... Severini Department of Mathematics and Department of Computer Science University of York, York YO10 5DD, U.K. ss54@york.ac.uk Richard C. Wilson Department of Computer Science University of York, York ... We describe some structural properties of the digraph D obtained from U 3 .InSection4,we list the sets of strongly regular graphs for which the eigenvalues of D successfully...

Ngày tải lên: 07/08/2014, 13:21

... journal of combinatorics 13 (2006), #R57 6 Proof of Lemma 2.9. Let α −β be a follower of γ −δ.Wesaythatα−β is safe if Left can survive both α − H and H − β moving second, for some follower H of G. ... + over modulo Inf. The importance of this observation stems from the fact that S contains a great many idempotents. Several of these are listed in Figure 8 of [10]. A typical examp...

Ngày tải lên: 07/08/2014, 13:21

... no vertex of T 0 is adjacent to any vertex of L. The distance of any vertex in T 0 from the farthest vertex in C is at most r + i/2. The distance of any vertex in the previous copies of T r p in ... journal of combinatorics 18 (2011), #P108 3 of degree one and let v be any such vertex of G. Set G ′ = G \ v. We may assume that H contains an induced copy of G ′ . Denote this c...

Ngày tải lên: 08/08/2014, 14:23

... new collection L  of lists of size 2 for G  = (V  , E  ) in the following way. The lists of the edges do not change (except for the fact that there are (n − 1) less of such lists). For each ... 05C78 Abstract Suppose the edges and the vertices of a simple graph G are assigned k-element lists of real weights. By choosing a representative of each list, we specify a vertex co...

Ngày tải lên: 08/08/2014, 14:23

... proved by Br´egman [2] (c.f. also [1] for a probabilistic description of a proof of Schrijver). Indeed, the Minc conjecture states that the permanent of an n by n matrix A with (0, 1) entries satisfies per(A) ... The solution of the van der Waerden problem for permanents, Dokl. Akad. Nauk SSSR 258 (1981), 1041-1044. [4] D. I. Falikman, A proof of van der Waerden’s conjecture on the p...

Ngày tải lên: 07/08/2014, 06:22

... journal of combinatorics 10 (2003), #R11 10 Proof: Let S = {x 1 ,x 2 , ··· ,x k } be an ordered subset of the vertices of G.LetC be a cycle of maximum order 2c containing all vertices of S in ... contradiction to the above inequality. Let c be the number of elements of S that are not vertices on any of the k + t edges of the matching. Then t + d + c of the edges are free....

Ngày tải lên: 07/08/2014, 07:21