Báo cáo toán học: "Regular factors of regular graphs from eigenvalues" pptx

... for classifying one-factorizations of regular graphs are studied. The smallest open case is currently graphs of order 12; one-factorizations of r -regular graphs of order 12 are here classified for ... bijection between the vertices of the graphs that maps one -factors onto one -factors; such a bijection is an isomorphism. The problem of classifying one-factorizations...

Ngày tải lên: 07/08/2014, 08:22

... L. Now we weight the edges of some part of the graphs from C. Subsequently, for the elements of C, set weights (i, −i) to the pairs of their edges (establishing the weights of their closed vertices ... P o 3 }-factor of a graph G is a collection of vertex (and edge) disjoint subgraphs of G which are either paths of lengths 1 or 2, or open paths of length 2 (we call the...

Ngày tải lên: 07/08/2014, 21:20

... collinearity graphs of) regular near polygons are regarded as one of the main classes of distance -regular graphs. The parameters of a regular near polygon must satisfy a number of restrictions, ... parameters of the regular near polygon. A near 2d-gon, d  2, is regular the electronic journal of combinatorics 17 (2010), #R149 1 Let x be a point of S. If y 1 and y...

Ngày tải lên: 08/08/2014, 12:23

... partitioning of the edges of a graph into 1 -factors is a 1-factorisation. A 1-factorisation is perfect if the union of any two of its 1 -factors is a single (Hamiltonian) cycle. For a full discussion of ... factorisations, see Chapter 11 of [14]. One of the ideas there is that of a train, which we now define for factorisations of complete bipartite graphs. Suppose we hav...

Ngày tải lên: 07/08/2014, 06:20

... [PY00] Peng and Yan investigate the linear discrepancy of strongly unimodular 0, 1 matrices. One part of their work is devoted to the case of basic strongly unimodular 0, 1 matrices, i. e. strongly ... Multiskalenmethoden’, Deutsche Forschungsgemeinschaft the electronic journal of combinatorics 7 (2000), #R48 4 matrices into incidence matrices of digraphs. Disc. Math., 102:143–147,...

Ngày tải lên: 07/08/2014, 06:20

... Subclaims, the proof of our lemma is complete. 5 Proof of the Main Theorem In this section, we present the proof of the main theorem. Let C be a topologically closed class of graphs with den(G) ... member of the second coordinate of the label of y, delete the edge x j y.If the digit of z is 3 and y is not a member of the second coordinate of the label of z, delete the...

Ngày tải lên: 07/08/2014, 06:23

... height of a vertex is defined to be its distance from the root. A vertex w is called a descendant of a vertex v (or v is called an ancestor of w)ifthe heights of the vertices on the unique path from ... ordering of the vertices to an ordering of the edges lexicographically. A broken circuit of H ⊆ G is a set of edges B ⊆ H such that there is some edge e ∈ G, smaller than ev...

Ngày tải lên: 07/08/2014, 08:22

... x of F 3 induces a valuation f x : F 1 → N; y → d(x, y) − d(x, F 1 )ofF 1 . So, we can distinguish the points of F 3 by means of the type of valuation of F 1 they induce. From this point of ... classes of valuations. (1) For every point x of S,themapf x : P→N; y → d(x, y) is a valuation of S.We call f a classical valuation of S. (2) Suppose O is an ovoid of S, i.e.,...

Ngày tải lên: 07/08/2014, 13:21

... University Press, 1987. the electronic journal of combinatorics 16 (2009), #N32 6 Skew Spectra of Oriented Graphs Bryan Shader Department of Mathematics University of Wyoming, Laramie, WY 82071-3036, USA email: ... underlying graph of G σ , and we denote by Sp(G) the adjacency spectrum of G. S kew-adjacency matrix S(G σ ) of G σ is intro duced, and its spectrum Sp S (G σ ) is...

Ngày tải lên: 07/08/2014, 21:21

... Betti numbers of ∆ (over K). The link of ∆ with respect to F ∈ ∆ is the simplicial complex lk ∆ (F ) = {G ⊂ [n] \F : G ∪F ∈ ∆}. In the study of face vectors of simplicial complexes, one of important ... characterization of h-vectors of Buchsbaum complexes of a special type including all 2-dimensional connected Buchs- baum complexes, and proved the necessity of the conjecture...

Ngày tải lên: 07/08/2014, 21:21