Báo cáo toán học: "Game chromatic number of Cartesian product graphs" ppsx

... for the 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 ... prove our results for graphs of odd girth at least 7. Dealing with graphs with larger odd girth will simply require a generalisation of this argument. Theo...

Ngày tải lên: 07/08/2014, 06:20

... Denley’s Theorem 4. References 1. Denley, T., The Independence number of graphs with large odd girth, The Electronic Journal of Combinatorics 1 (1994) #R9. 2 We can now prove the following theorem. Theorem ... is sharp for the regular complete bipartite graphs K aa . The above results are readily extended to graphs of larger odd girth. Lemma 2: Let G have odd girth...

Ngày tải lên: 07/08/2014, 06:20

... the number of partitions of (the number) n,andQis its ordinary generating function. Also, define p(n, k) to be the number of partitions of n with largest part at most k. We will have use of the ... values of n, we shall use elementary estimates and some well-known bounds for ordinary partitions (of a number) to express most values of b n in terms of the number...

Ngày tải lên: 07/08/2014, 06:20

... +1) 6 49n 6 . 7. The number of ascendants of a given node in a LBST As in the case of the number of ascendants in a random BST, computing the probability that the j th node in a random LBST has m ascendants ... other random variables: the number of descendants D n and the number of ascendants A n of a randomly chosen internal node...

Ngày tải lên: 07/08/2014, 06:22

... n)k −1 φ(k). In either case, the inequality in part 1 of the lemma holds. On the number of perfect matchings and Hamilton cycles in -regular non-bipartite graphs Alan Frieze ∗ Department of Mathematical ... of combinatorics 7 (2000), #R57 4 3 Hamilton Cycles A Hamilton cycle is the union of two perfect matchings and so h(G) ≤ 1 2 m(G) 2 a...

Ngày tải lên: 07/08/2014, 06:22

... tight. The odd edge-connectivity of a graph G is the size of a smallest odd edge cut of G.The odd girth of G is the length of a shortest odd cycle of G. Zhang [19] proposed a strengthing of Jaeger’s ... of length at least 2k. For otherwise, for any internal vertex x of a thread of length the electronic journal of combinatorics 8 (2001), #R25 3 Circular chromati...

Ngày tải lên: 07/08/2014, 06:22

... in the case when m is prime. Whether a permutation of n admits an m-th root can be read on the partition of n determined by the lengths of the permutation’s cycles, because the class of such the ... is the exponential generating function (EGF, formal series) of the m-thpowersinthegroups n . This means that the number of m-thpowersin n is p n (m)ìn!foreachn....

Ngày tải lên: 07/08/2014, 06:23

... inequalities are the numbers v k of vertically indecomposable distributive lattices of size k. We present the explicit values of the numbers d k and v k for k<50 and prove the following exponential bounds: 1.67 k <v k < ... lattices, one rather considers the vertical sum in that case, where the only difference to the former is that now the top element  1 of...

Ngày tải lên: 07/08/2014, 06:23

... monotone subsequences of length 3 in L, R are also such subsequences of S.There are no monotone subsequences of S containing both 0 and n − 1. There are no monotone subsequences of S of the form a, ... up of k monotone descending subsequences, each of length n/k or n/k; clearly it has no monotone ascending subsequences of length k +1, and any monotone descendin...

Ngày tải lên: 07/08/2014, 07:21

... we are not in one of these cases, then there is exactly one edge e attached to v which is below l.Theedgee is on a loop of the configuration. Let us start with e and follow the part of the loop ... which is based on a variation of the above reasoning, see Section 5. Finally, for the proof of the more specific assertions in Conjectures 1.1 and 1.2 on the i...

Ngày tải lên: 07/08/2014, 08:22

... x and y to be row and column sums of a matrix is that they have the same weight. Clearly, the row sums of a member of M are at most n.Conversely,ifx =(x 1 , ,x m ) and 0 x i n,letR = R(x)bethem ... (5) the electronic journal of combinatorics 13 (2006), #N8 5 3 Start of the proof Let N = {0, 1, }. Define the weight of a matrix N to be the sum of its e...

Ngày tải lên: 07/08/2014, 13:21

... listed in π s,m n−1 .Sincen is the largest number, this forces the insertion point to be right at the beginning of the list. Since π  is precisely π s,m n−1 with m = n−1−s 2 , this yields the permutation ... from the proof of Theorem 1.3, as if the structure of a permutation is ‘close’ to that of π s,m n then the configuration of the first type in Figure 2...

Ngày tải lên: 07/08/2014, 13:21

... square all-1 matrix. Proof of Theorem 1.1: The square of the number of perfect matchings of G counts ordered pairs of such matchings. We claim that this is the number of spanning 2-regular subgraphs ... Cuckler and J. Kahn, Entropy bounds for perfect matchings and Hamiltonian cycles, to appear. [3] S. Friedland, An upper bound for the number of perfect matching...

Ngày tải lên: 07/08/2014, 15:22

... (2.6) and (2.8), the number of copies of K k in E is (1 + o(1)) |E| k k! q − ( k 2 ) . . This implies that the number of the number of k-tuples of k mutually orthogonal vectors in E is also (1 ... o(1)) |E| k k! q − ( k 2 ) , completing the proof of Theorem 1.2. Acknowledgments The research is performed during the authors visit at the Erwin Schrăodinger I...

Ngày tải lên: 07/08/2014, 15:22

... 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 ... for every n ≥ 2. Hence the existence of an upper bound for the game chromatic number of the Cartesian product of graphs in terms of game chromatic numbers of fa...

Ngày tải lên: 07/08/2014, 21:20