Báo cáo toán học: "Distinguishing Chromatic Numbers of Bipartite Graphs" pps

... 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 conjecture, ... 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 chromatic...

Ngày tải lên: 07/08/2014, 06:22

... (V C ,C)ofG(V,E). The set C of all cycles forms a subspace of (E, ⊕, ·) which is called the cycle space of G.AbasisBof the cycle space C is called a cycle basis of G(V, E) [2]. The dimension of the ... minimal cycle basis of G. The remainder G ∗ of G after all cycles C β , β ∈ K are removed by the above procedure is composed of Y ∗ and those edges of H that are not contained...

Ngày tải lên: 07/08/2014, 06:22

... electronic journal of combinatorics 14 (2007), #N21 2 3.2 Proof of part II For proving part II of the theorem we want to construct a class of balanced bipartite graphs the elements of which cannot ... Proof of Theorem 1 We will show the two parts of the theorem in separate subsections. 3.1 Proof of part I Observe, that since we are looking for a spanning regular subgraph, th...

Ngày tải lên: 07/08/2014, 15:22

... id}.Callm(σ)themotion of σ and m(G)themotion of G. Using an appealing probabilistic argument Russell and Sundaram showed that if the motion of G is large, then the distinguishing number of G is small. ... x.An automorphism might take x to any of the n r vertices. Once the image of x is chosen, then a clique that contains x can be mapped to a clique that contains the image of x i...

Ngày tải lên: 07/08/2014, 08:22

... chromatic index of special classes of graphs has been of interest. For example the circular chromatic index of the flower snarks is studied in [3] and the circular chromatic index of Goldberg snarks ... edge (3 + ε)– colouring of this graph, the difference between the colours of the semiedges a  and b  of the first copy of B, and the semiedges a and b of the last copy...

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... R as ES =1. The proof of this result is given in Sec. 3 and is based on some estimations (obtained in Sec. 2) of the cardinality of cuts for almost every graph. 2. Estimations of the Cardinality of Cuts We ... cardinality of the U −cut C U (G)ofG; c U (n) - the mean value of c U (G)overG n , i.e., c U (n)= 1 p  p i=1 c U (G i ); c(G) - the cardinality of a maximum cut of G,...

Ngày tải lên: 06/08/2014, 05:20

... 476.13014). [199] J. Hofbauer. A short proof of the Lagrange-Good formula. Discr. Math., 25:135–139, 1979. (MR 81e:05019). [200] J. Hofbauer. A representation of Sheffer polynomials in terms of a differential ... terms of x n via Taylor’s theorem f(x + a) = ∞  n=0 a n D n f(x) n! , The Electronic Journal of Combinatorics, #DS3 Update of April, 2000 29 [389] G C. Rota. The number o...

Ngày tải lên: 07/08/2014, 05:23