Báo cáo toán học: "Chromatically Unique Multibridge Graphs" potx

... C.C.Rousseau and R.H.Schelp, Ramsey minimal graphs for star forests, Discrete Math. 33 (1981), 227–237. [4] S.A.Burr, P.Erd˝os, R.J.Faudree, C.C.Rousseau and R.H.Schelp, Ramsey minimal graphs for match- ings,inThe ... Threshold functions for Ramsey properties,submitted. Key words and phrases: critical graphs, Ramsey theory 1991 Mathematics Subject Classifications: 05D10, 05C80 4 O...

Ngày tải lên: 07/08/2014, 06:20

... and φ cannot be distinguishing. This contradicts our assumption that φ is an r-distinguishing labeling. ✷ We remark that this proves that the largest integer in D(S 3 )is3,since the subgroups ... the goal is to minimize the number of colors used. Consequently we define the distinguishing number of a graph G by D(G)=min{r | G has a labeling that is r-distinguishing}. The original key problem...

Ngày tải lên: 07/08/2014, 06:20

... the class of all 4-chromatic graphs. The structure of the red graph is obvious by Corollary, but we do not know which graphs can occur as blue graphs and what are the properties of graphs in which ... on the Wall, a list of conjectures of Graffiti. Ramseyan Properties of Graphs by Ermelinda DeLaVina delavina@math.uh.edu Siemion Fajtlowicz siemion@math.uh.edu Uni...

Ngày tải lên: 07/08/2014, 06:20

... The notion of orthogonal colorings is strongly related to the notion of orthogonal Latin squares. The orthogonal chromatic number of G, denoted by Oχ(G), is the minimum possible number of colors ... 2, 3, 1, 3). The notion of k -orthogonal colorings is strongly related to the notion of orthogonal Latin squares. Recall that two Latin squares L 1 ,L 2 of order r are...

Ngày tải lên: 07/08/2014, 06:20

... parts are all of size one. Alternately, the complement of such a graph either has no edges or consists of the the disjoint union of three or fewer complete graphs. Proof. The complement of K − 5 is ... similar proofs for complexes of dimension 2 and higher. We conjecture that the answer is “yes,” but the complexity of the proof would be astronomical, even for dimension 2. Hidden...

Ngày tải lên: 07/08/2014, 06:20

... 68W25. Keywords: graph coloring, online algorithms. Abstract The problem of online coloring an unknown graph is known to be hard. Here we consider the problem of online coloring in the relaxed ... independence number α are known in advance. The unknown case can be handled via a doubling technique, see [5]. Without loss of generality, α ≥ n/ log n.Letq =(1/2) log n/α n. Before colori...

Ngày tải lên: 07/08/2014, 06:20

... shown that cubic graphs with arbitrarily large girth exist (see Theorem 3.2) and so there is a well-defined integer à 0 (g), the smallest number of vertices for which a cubic graph with girth ... account of the problem of constructing cubic graphs with large girth. There is a well-dened integer à 0 (g), the smallest number of vertices for which a cubic graph with gi...

Ngày tải lên: 07/08/2014, 06:22

... chromatically unique if a k <a 1 + a 2 , and find examples showing that θ(a 1 ,a 2 , ···,a k )maynotbe chromatically unique if a k = a 1 + a 2 . Keywords: Chromatic polynomials, χ -unique, χ-closed, ... θ(a 1 ,a 2 , ···,a k ) is χ -unique if a i ≥ k − 1 for i = 1, 2, ···,k. ✷ Theorem 2.3 ([11]) Let h ≥ s +1≥ 2 or s = h +1. Then for k ≥ 5, θ(a 1 ,a 2 , ···,a k ) is χ -unique if a 2 − 1...

Ngày tải lên: 07/08/2014, 08:20

... be the product of the weights of all the edges in the matching. Then the weight of the Aztec graph A is (A)=  m (m), the sum over all matchings of A. Using the tilted version of the Aztec diamond ... 1)-order Aztec diamond subgraphs A NW , A SW ,andA SE .LetA mid be the (n − 2)-order Aztec diamond subgraph of A lying directly in the middle, concentric wi...

Ngày tải lên: 07/08/2014, 08:20

... , proving (8). Inequality (9) follows easily, since, in fact, for every p>3, the function g (x)hasa local minimum at 0. ✷ 5 H-free graphs In this section we are going to prove the following ... (5), we obtain that (r −1)  n p +1  +  2n p +1  <n. Letting n →∞, we see that p ≥ r, contradicting the assumption and completing the proof. ✷ Maximizing independently each summand in...

Ngày tải lên: 07/08/2014, 08:20

... |Γ|≤m! and the subset {y 1 , ,y j } satisfies 1. φ(y i )=i for each i, 2. y i+1 is in Γ i−1 .y i for each i from 2 to j − 1, and y 1 is in Γ j−1 .y j , then j ≤ m and |Γ i−1 .y i |≥j − i + 2for each ... shows this and two other graphs with the same automorphism group and demonstrates that all three have different distinguishing numbers. This example disproves a conjecture in [...

Ngày tải lên: 07/08/2014, 08:20

... irregular graphs, Graphs and Combinatorics 18 (2002), 53–57. [2] N. Biggs, Algebraic Graph Theory, Cambridge University Press, Cambridge, second edition, 1993. [3] J.A. Bondy, M. Simonovits, Cycles ... vine on P ∗ and P ∗ is the unique uv-geodesic. Proof. Suppose, for a contradiction, that H is not a vine on P ∗ .Letx ≺ v be a vertex of P ∗ at a maximum distance from u on P ∗ such th...

Ngày tải lên: 07/08/2014, 08:22

... |G| ≤ .  We note that an infinite locally finite graph can have infinite distinguishing number. For a simple example consider the graph that is obtained from the one-way infinite path v 0 , v 1 , ... the infinite case and find many similarities. We also determine the distinguishing number of infinite hypercubes of arbitrary dimension. To this end we take recourse to elementary results abo...

Ngày tải lên: 07/08/2014, 15:22

... 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

... Hence, the class of (maximal) planar graphs is contained in the class of maximal K 3,3 -minor-free graphs and we can use the number of planar graphs and the number of triangulations as lower bounds. ... preliminary version available at http://algo.inria.fr/flajolet/Publications [7] O. Gim´enez and M. Noy. The number of planar graphs and properties of random planar...

Ngày tải lên: 07/08/2014, 21:20