Báo cáo toán học: "Circular chromatic number of planar graphs of large odd girth" docx

... 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 ... no thread 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...

Ngày tải lên: 07/08/2014, 06:22

... 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 factors would imply that there is ... examples of spanning subgraphs with the game chromatic number arbitrarily larger than in their original graphs (e.g. complete bipartite graphs minus a perfect matching as...

Ngày tải lên: 07/08/2014, 21:20

... 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 ... find large independent sets in graphs with large odd girth at. To illustrate the ideas behind this algorithm we shall first prove our results for graphs of odd girth...

Ngày tải lên: 07/08/2014, 06:20

... 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 2k + 1 or greater (k ≥ 2). Then α(G) ... 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...

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 of ord...

Ngày tải lên: 07/08/2014, 06:20

... JOURNAL OF COMBINATORICS 5 (1998), #R20 8 3. The number of descendants in random BSTs The number of the descendants D n,j of the j th node of a BST of size n is recursively computed as the number of ... 1998. Abstract. The number of descendants of a node in a binary search tree (BST) is the size of the subtree having this node as a root; the number of ascendant...

Ngày tải lên: 07/08/2014, 06:22

... argue the existence of a 6-cycle as in the previous case. Remark: The proof shows that the number of Hamilton cycles is within a poly- nomial factor of the number of two factors of G. Therefore one ... is a pair of cycles of lengths a and b + c; 4. for at most n i choices, C i ⊕C is a pair of cycles of lengths c and a + b; 5. for at most n i choices, C i ⊕C is a triple...

Ngày tải lên: 07/08/2014, 06:22

... singularities of R m form a dense subset of the unit circle. The argument given to reach the desired asymptotics uses the convergence of the series of coefficients of R m , and a combination of monotonic ... the asymptotics of the coefficients of C m =  n c n (m)X n because C m has a finite number of algebraic singularities on its circle of convergence. This asymptotics turn...

Ngày tải lên: 07/08/2014, 06:23

... a downward numbering of elements. Of course, an upward numbering would work as well. Here, an n-poset is a poset P with underlying set n = {0, ,n− 1}. We write i ≺ j if j is a cover of i in P ... to isomorphism by a finite number of “doublings” of principal filters. Theorem 3 Every distributive lattice (D, ) of finite cardinality k>1 and height n is isomorphic to a lattice of...

Ngày tải lên: 07/08/2014, 06:23

... do not minimise the number of monochromatic triangles over all colourings (that is, the colourings minimising the number of monochromatic triangles do not correspond to pairs of transitive tournaments). ... number be known as M k (n). I conjecture that this is in fact the minimum number of monotone subsequences of length k +1. the electronic journal of combinatorics 9(2) (...

Ngày tải lên: 07/08/2014, 07:21