Báo cáo toán học: "Unit distance graphs with ambiguous chromatic number" pot

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Ngày tải lên: 05/08/2014, 09:46

... ✷ Summarizing, we now know all extremal graphs, G with f (G)=2δ +1. The connected extremal graphs are those given in Theorem 3 along with the trivial ones with only 2δ + 1 vertices. We noticed that ... the sense that there exist graphs of minimum degree δ with no longer paths. Our purpose in this article is to characterize all such extremal graphs. For a graph G with...

Ngày tải lên: 07/08/2014, 06:20

... towards accounting for the wastefulness of the first moment method. Instead of Almost all graphs with 2.522n edges are not 3-colorable Dimitris Achlioptas ∗ optas@cs.toronto.edu Michael Molloy † molloy@cs.toronto.edu Department ... in that the selection is done with replacement, i.e. multiple edges are allowed. We will denote this model by G r (n, m). Intuitively, it is cl...

Ngày tải lên: 07/08/2014, 06:20

... Section 2 we construct our main tools to study the Erd˝os problem over finite Euclidean and non -Euclidean spaces, the finite Eu- clidean and non -Euclidean graphs. Our construction follows one of Bannai, ... concise, we will restrict our discussion to the finite non- Euclidean graphs obtained from the action of the simple orthogonal group on the set of non-isotropic p...

Ngày tải lên: 07/08/2014, 15:22

... electronic journal of combinatorics 14 (2007), #R50 6 Reversal Distance for Strings with Duplicates: Linear Time Approximation using Hitting Set Petr Kolman ∗ Charles University in Prague Faculty ... (approximately) the Minimum Hitting Set problem: Φ ← a hitting set for (U, S) transform the hitting set into a common partition: A, B ← for each duo xy ∈ Φ, cut all...

Ngày tải lên: 07/08/2014, 15:22

... combinatorics 14 (2007), #R 51 10 Table II. Bounds on K(r, s, s; 2) for r ≤ 16 and 9 ≤ s ≤ 16 . s = 9 s = 10 s = 11 s = 12 s = 13 s = 14 s = 15 s = 16 r = 1 9 10 11 12 13 14 15 16 r = 2 16 B 18 B 20B ... 71F 72F a85E a96 − 98E a103 − 11 3E 11 0 − 12 6G r = 13 60 − 65C 66 − 72C 73 − 81F 79 − 84C 85F a98E 10 5 − 11 3E a 117 − 12 8E r = 14 63 − 67C 70 − 76C 77...

Ngày tải lên: 07/08/2014, 15:22

... = |U 0 | + 1. Thus all Zelinka graphs have toughness less than one. 3 Maximal nontraceable graphs with toughness less than one Suppose P is a path in a graph G, with endvertices a and z. If we ... of 2-connected non-Zelinka MNT graphs with toughness less than 1. the electronic journal of combinatorics 15 (2008), #R18 2 Maximal Nontraceable Graphs with T...

Ngày tải lên: 07/08/2014, 15:23

... past twenty years, rectangle visibility graphs have generated consider- able interest, in part due to their applicability to VLSI chip design. Here we study unit rectangle visibility graphs, ... 1985. [13] T. Shermer. On rectangle visibility graphs II: k-hilly and maximum-degree 4. Manuscript, 1996. [14] T. Shermer. On rectangle visibility graphs III: external visibility and...

Ngày tải lên: 07/08/2014, 21:20

... graph G, we let ∆(G) denote its maximum degree. One of the natural lines of investigation for Laplacian integral graphs is to focus on graphs for which the maximum degree is not very large. It is ... (3) Figure 5: connected, non-regular, Laplacian integral graphs with maximum degree 3 the electronic journal of combinatorics 15 (2008), #R120 6 Figure 41: graphs arisin...

Ngày tải lên: 07/08/2014, 21:20

... construct a new class of graphs with ambiguous chromatic numb er. They are unit distance graphs with vertex set R n , and hence may be seen as further evidence that the chromatic number of the ... the following. the electronic journal of combin atorics 16 (2009), #N31 3 Unit distance graphs with ambiguous chromatic number Michael S. Payne ∗ School of Mathematical Sc...

Ngày tải lên: 07/08/2014, 21:21

... 1: Numbers of chromatic polynomials of degree at most 10. (A) Total number of chromatic polynomials, (B) number of chromatic polynomials of clique-separable g r aphs and (C) number of chromatic ... 4705 Table 2: Chromatic factorisations of chromatic polynomials of degree n ≤ 10 of strongly non-clique-separable graph. 4 Certificates of Factorisation Definition A...

Ngày tải lên: 07/08/2014, 21:21

... theorem, Discrete Math. 308 (2008), no. 19, 4337–4360. [21] R. Martin, Y. Zhao, Tiling tripartite graphs with 3-colorable graphs: The extreme case, preprint. [22] A. Shokoufandeh, Y. Zhao, Proof of a ... contradiction.  the electronic journal of combinatorics 16 (2009), #R109 4 Tiling tripartite graphs with 3-colorable graphs Ryan Martin ∗ Iowa State University Ames, IA 5...

Ngày tải lên: 08/08/2014, 01:20

... (9) and (10) with V replaced by V ′ . Then ∆(V ′ m ) = C ′ σ with σ being the identity permutation and E ′ m the union of a ll C ′ σ with σ ∈ Sym(m) where C ′ σ = Cyl m (T ′ σ ) with T ′ σ = ... may exist even fo r non-isomorphic graphs. In any o f these cases the graphs are called equivalent (Definition 3.3). For example any two strongly regular graphs with the same parameters...

Ngày tải lên: 08/08/2014, 01:20

... X u )-DS of G. Hence, γ(G u ; X u ) ≤ |D v | + 1 = γ(G v ; X v ) + 1. ✷ the electronic journal of combinatorics 18 (2011), #P12 34 A new bound on the domination number of graphs with minimum degree ... is of interest to determine upper bounds on the domination number of a graph. In 1989, McCuaig and Shepherd [12] presented the beautiful result that...

Ngày tải lên: 08/08/2014, 12:23

... called cyclic defect’. Here we prove that this conjecture holds. Keywords: Graphs with cyclic defect, Moore bound, defect, repeat. 1 Nonexistence of graphs with cyclic defect Let G be a graph of ... electronic journal of combinatorics 18 (2011), #P71 4 Nonexistence of graphs with cyclic defect Mirka Miller ∗† School of Electrical Engineering and Comp. Science, Un...

Ngày tải lên: 08/08/2014, 14:22