Báo cáo toán học: "Sparse graphs usually have exponentially many optimal colorings" pps

... =  2 0 n 1/2 p 1/2 ln(np) . the electronic journal of combinatorics 9 (2002), #R27 5 Sparse graphs usually have exponentially many optimal colorings Michael Krivelevich ∗ Department of Mathematics, Sackler Faculty ... . The theorem is proven. ✷ We have thus proven that most of the graphs in the probability space G(n, p)with p = n −a ,1/3 <a<2, have exponentially m...

Ngày tải lên: 07/08/2014, 06:23

... <t− (k − 1)(s − 1) points. So we may suppose the round sets to have cardinality ≥ s.Ifnowk = 1 we have C(t − s). If k>1andp = 0 we have k(s − 1) <t, and hence k ≤ t−1 s−1 .Ifk>1and p>0letV ... with R(t, s) in a rather trivial way, will be said to have property R ∗ (t, s). If 2s ≥ t +2 we canonlyhave R ∗ (t, s)withk =1, thus if we have C(t − s). Clearly R(t, s) entai...

Ngày tải lên: 07/08/2014, 13:21

... statement, namely for bipartite graphs, was also conjectured in [5]. Several papers have app eared with proof s of Aldous’s con- jecture for some particular classes of graphs, and recently a beautiful ... Cayley graphs on the symmetric group generated by initial reversals have unit spectral gap Filippo Cesi Dipartimento di Fisica Universit`a ... provide a simple proof of this last as...

Ngày tải lên: 07/08/2014, 21:21

... studying the family of Cayley graphs for a given finite group G, which focuses attention on those graphs Γ for which N Aut(Γ) (G)istran- sitive on edges, and those undirected graphs Γ for which N Aut(Γ) (G) ... edge-transitive Cayley graph all elements of the set S have the same order, so these graphs are not normal edge-transitive. We show that these graphs are edge-transitive. In...

Ngày tải lên: 06/08/2014, 05:20

... P. Erd˝os and T. Gallai, Graphs with prescribed degrees of vertices (Hungarian), Math. Lapok 11 (1960), 264-274. [10] T. Gustavsson, Decompositions of large graphs and digraphs with high minimum ... North Carolina, Chapel Hill (1970) 428-450. [21] R. M. Wilson, Decomposition of complete graphs into subgraphs isomorphic to a given graph, Congressus Numerantium XV (1975), 647-659. the ele...

Ngày tải lên: 07/08/2014, 06:20

... exponentially? This question was answered by Grigorchuk, who constructed a family of groups whose Cayley graphs have intermediate growth [6]. See [8] for a nice description of these groups. Graphs ... the integers. We observe that all bounded degree ω-periodic graphs are amenable. We also provide examples of ω-periodic graphs which have exponential volume growth, non-linear po ly...

Ngày tải lên: 07/08/2014, 13:21

... v i ) ∈ B m− . Thus we have B m ˘ = B m+ for m ≤ . Then by making superficial changes to the remainder of the proof we establish the result for the nonsymmetric case. Thus we have the following: the ... γ ∈ L, (α, β, γ) ∈ M, then M is realized by a coloring on K ω , the complete graph on countably many vertices. Any such color α is called a flexible color, since it can participate in a...

Ngày tải lên: 07/08/2014, 15:23

... mutation-finite graphs from triangulations of ori- ented bordered surfaces with marked points. We will call such graphs “of geometric type”. Besides graphs with 2 vertices, and graphs of geometric ... further matching, x will have at least 2 neighbors which are only connected to x. the electronic journal of combinatorics 15 (2008), #R139 9 1.5 Graphs of extended affine types The foll...

Ngày tải lên: 07/08/2014, 21:21

... 05E99 Abstract We found the characteristic polynomials for all graphs on 12 vertices, and report statistics related to the number of cospectral graphs. 1 Introduction Let the spectrum of a graph be the ... isomorphism problem, it is of interest what fraction of all graphs is uniquely determined by its spectrum. Haemers conjectures that the fraction of graphs on n vertices with a cospe...

Ngày tải lên: 07/08/2014, 21:21

... eigenvalues of Sudoku graphs, which turn out to be integers. Hence, Soduku graphs belong to t he important class of integral graphs. Other examples of integral graphs are the complete graphs K n [2], ... AKCE J. Graphs. Combin., Vol. 2, No. 1, pp. 4 5–56, 2005. [18] Sander, T. On certain eigenspaces of cographs. Electron. J. Combin., Vol. 15, 2008. [19] Sciriha, I. Coalesced and Embe...

Ngày tải lên: 07/08/2014, 21:21