Báo cáo toán học: "Game list colouring of graphs" ppt

... 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

... 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

... purposes of proving that the game coloring number of Cartesian products is not bounded by a function of game coloring numbers of factor graphs. However the class of Cartesian products of stars ... the proof of this result more transparent, we introduce the so-called game of combinations which could also be of independent interest. At the end of this section we present some...

Ngày tải lên: 07/08/2014, 21:20

... 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

... suggests another view of the subject with focusing on the cardinality of monochro- matic symmetric subsets irrespective of the measure-theoretic aspects. § 7 contains a list of open problems. Techniques ... B ⊆ A of measure µ(B) ≥ µ(A) 2 . (SL) Every measurable set A ⊂ Ωofmeasure0<µ(A) < 1 contains a symmetric subset B ⊆ A of measure µ(B) >µ(A) 2 . (U) ms(Ω,r) ≤ 1/r 2 ....

Ngày tải lên: 07/08/2014, 06:22

... [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

... 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

... 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

... chromatic number of graphs. A natural generalization of chromatic number to digraphs was introduced by Neumann -Lara in [21]. A (proper) colouring of a digraph D is a colouring of the vertices of D so that ... Neˇsetˇril and Sopena [20] defined the colouring game of oriented graphs, which is the same as the colouring game of undirected graphs, except that a partial colou...

Ngày tải lên: 08/08/2014, 11:20

... concept of list colorings. This generalization is based on a different point of view. Instead of assigning color lists L v of size ℓ v to the vertices v of a (hyper)graph, we assign sets of vertices ... number of bipartite graphs. This theorem on its own achieved some prominence in the theory of list colorings, and the upper bound of the list chromatic number for bipart...

Ngày tải lên: 08/08/2014, 12:23