Báo cáo toán học: "Star coloring high girth planar graphs" ppt

Báo cáo hóa học: " Research Article High Girth Column-Weight-Two LDPC Codes Based on Distance Graphs" potx

... of interconnections and destinations is re-duced. Addressing within a group is also simpliﬁed. With oneknown row-column connection in submatrix, the rest of thesubmatrix connections could ... varying vertex degrees and girths produce column-weight-two LDPC codes of diﬀerent girths and rates.For a graph of size n,vertexdegreeofk,andgirthofg, thecorresponding LDPC code matrix is of size ... performances of high girth LDPC codes from dis-tance graphs (25 iterations).formances approaching BER of 10−6between 5 and 6 dB forsome codes. Figure 2 shows performance curves for codes de-rived...

Báo cáo toán học: "THE INDEPENDENCE NUMBER OF DENSE GRAPHS WITH LARGE ODD GIRTH" ppsx

... Denley’s Theorem 4.References1. Denley, T., The Independence number of graphs with large odd girth, The Electronic Journal of Combinatorics 1 (1994) #R9. 2We can now prove the following theorem.Theorem ... is sharp for the regular completebipartite graphs Kaa.The above results are readily extended to graphs of larger odd girth.Lemma 2: Let G have odd girth 2k + 1 or greater (k ≥ 2). Thenα(G) ... dk−1(v))1+d1(v)+···+ dk(v).Proof. Randomly label the vertices of G with a permutation of the integers from 1 ton.LetA (respectively B) be the set of vertices v of G such that the minimum label...

Báo cáo toán học: "Online Coloring Known Graphs" docx

... 68W25.Keywords: graph coloring, online algorithms.AbstractThe 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) logn/αn. Before coloring, randomly ... Gyárfás and Lehel [4]holds also for our model of a known input graph.Bartal et al. [2] considered a different version of online coloring a known graph. Intheir model, each presented vertex is...

Báo cáo toán học: "Circular chromatic number of planar graphs of large odd girth" docx

... tight.The odd 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 ... of length at least 2k. For otherwise, for any internal vertex x of a thread of lengththe electronic journal of combinatorics 8 (2001), #R25 3 Circular chromatic number of planar graphs of large odd ... Klostermeyer and C.Q.Zhang, (2+)-coloring of planar graphs with large odd girth,J. Graph Theory, 33(2000), 109-119.[10] D. Moser, The star chromatic number of planar graphs, J. Graph Theory, 24 (1997),33-43the...

Báo cáo toán học: "The Neighborhood Characteristic Parameter for Graphs" pptx

... − 15 + 12 − 3=0N char(dodecahedron) = 20 − 60 + 20 = −202 Computing the Neighborhood Characteristic The neighborhood characteristic of a graph can also be calculated in terms of the completebipartite ... overcounting is corrected for in the following theorem (which alsoshows that, for a bipartite graph G,N char(G) equals twice the ‘bipartite characteristic deﬁned in [5]).Theorem 1 For every graph G ... singletons of Bjform a standard basis, dim(B0)=n,dim(B1)=m,dim(B2)=k2,2,dim(B3)=k2,3, and for j ≥ 4, dim(Bj)=iki,j−i+2over all i for which2 ≤ i<j. For each j ≥ 1, taking...

Báo cáo toán học: "On Hypergraphs of Girth Five" pdf

... of a cycle or a union of cycles of the permutation π : x → 2x of Zn(the map isa permutation since gcd(2,n) = 1). Only one cycle of D (and of π) has length 1, namely{0}.Foreachm-cycle C of ... family of all k-cycles byCk. For example, a 2-cycle consists of a pair of vertices and a pair of edges such that thepair of vertices is a subset of each edge. The above deﬁnition of a hypergraph ... problem of estimating the size of hypergraphs of given girth with certain generalized Tur´an numbers. It is easy to see that T3(n, 4, 2) andT3(n, 6, 3) are precisely the maximum number of edges...

Báo cáo toán học: "Regular spanning subgraphs of bipartite graphs of high minimum degree" docx

... referee for the useful remarks.the electronic journal of combinatorics 14 (2007), #N21 6 Regular spanning subgraphs of bipartite graphs of high minimum degreeB´ela Csaba∗†Submitted: Aug 1, 2007; ... electronic journal of combinatorics 14 (2007), #N21 2 3.2 Proof of part IIFor proving part II of the theorem we want to construct a class of balanced bipartite graphs the elements of which cannot ... regular) bipartite graphs with large minimum degree,for f ≡ r.∗Analysis and Stochastics Research Group of the Hungarian Academy of Sciences, University of Szeged,Hungary and Department of Mathematics,...

Báo cáo toán học: "Induced paths in twin-free graphs" pptx

... minimalr -twin-free graph for the induced subgraph relationship. Indeed, we have:the electronic journal of combinatorics 15 (2008), #N17 5 An r -twin-free graph contains a path P2r+1as an induced ... vertices in graphs, IEEE Transactions on Information Theory, vol 44, pp.599-611, 1998.[6] A. Lobstein, Bibliography on identifying and locating-dominating codes in graphs,http://www.infres.enst.fr/∼lobstein/debutBIBidetlocdom.pdf[7] ... r-identifyingcodes. We show that if a graph G is r -twin-free, then it contains a path on 2r + 1vertices as an induced sugbraph, i.e. a chordless path.keywords: graph theory; identifying codes; twin-free...

Báo cáo toán học: "Large holes in quasi-random graphs" pptx

... checking if the given graph is (d; ε1, ε2)-regular we need to consider only sets of thesize ε1|Vi|, i = 1, 2. In the following section we state our main results proved in Sections 3. In ... counting edges between sets U and W . Note, that each of theserandom variables has the same binomial distribution with expected value à = |U||W |d =2n2d. Applying Chernoﬀ’s inequality (see inequality ... bipartite subgraph that can be contained in a (d; ε)-regular graph.3 The Proof of Theorem 2.1Before we prove Theorem 2.1, we state a result showing how, by using random graphs,one can ﬁnd a (d;...

Báo cáo toán học: "Star coloring high girth planar graphs" ppt

... that any planar graph has a star coloring with k colors.While Corollary 4.2, Corollary 3.2, and [10] improve upon the upper bounds for planar graphs of high girth, less is known about planar graphs ... every planar graph of girth at least 5 can be star colored using 16 colors, every planar graph of girth at least 7 can be star colored with 9 colors, and planar graphs of suﬃciently large girth can ... combinatorics 15 (2008), #R124 3 4 Girth 9 planar graphsTo prove that girth 9 planar graphs can be star colored with 5 colors, we use a similarapproach as used for girth 14 planar graphs, except that...

Báo cáo toán học: "On Coloring the Odd-Distance Graph" pdf

... θ increasesfrom 0 toπ2. Also, the signs of these integrals alternate, so we can either throw out allof them or all but the ﬁrst one, depending on whether the integral of h across R⌊rπ⌋ispositive ... establishes that the measurable chro matic number of the odd-distance graph is inﬁnite.4 Conclus i on and Open Problems The largest remaining question is whether or not the chromatic number in the normalsense ... Introducti onLet O be the graph with V (O) = R2and where two vertices are connected if they are atan odd distance from each other. We call O the odd-distance graph. Let the measurablechromatic...

Báo cáo toán học: "Bartholdi Zeta Functions of Fractal Graphs" pptx

... proof of Theorem 1, and discussed threediﬀerent zeta functions of any graph. Various proofs of Bass’ theorem were known. Kotaniand Sunada [15] proved Bass’ theorem by using the property of ... Ihara zeta function of a fractal graph, and gave a determinant expression of it. We deﬁne the Bartholdi zeta function of a fractal graph, and present its determinant expression.1 Introduction Zeta ... Introduction Zeta functions of graphs started from p-adic Selberg zeta functions of discrete groups byIhara [14]. At the beginning, Serre [20] pointed out that the Ihara zeta function is the zeta function of...

Báo cáo toán học: "The Laplacian Spread of Tricyclic Graphs" ppt

... graphs with maximum Laplacian spread among all tricyclic gr aphs of order n ≥ 11. Moreover, fo r 5 ≤ n ≤ 10,if G is one with maximum Laplacian spread of all tricyclic gra phs of order n, then G ... vertices of the star,respectively [4].A tricyclic graph is a connected graph in which the number of edges equals the number of vertices plus two. In this paper, we study the Laplacian spread of tricyclic ... the spread of a graph, which are some improvements of Gregory’s bound on the spread for graphswith additional restrictions.Here we consider another version of spread of a graph, i.e. the Laplacian...

Báo cáo toán học: "On Universal Cycles of Labeled Graphs" ppt

... notion of universal cycles. In particular, we show thatthese cycles exist for certain classes of labeled graphs. In order to define a universal cycle of graphs, we must first extend the notion of ... Classification: 05C30AbstractA universal cycle is a compact listing of a class of combinatorial objects. Inthis paper, we prove the existence of universal cycles of classes of labeled graphs,including ... 3-window of an 8 vertex graph.Definition 1.2. Given F, a family of labeled graphs on k vertices, a universal cycle (U-cycle) of F, is a labeled graph G such that the sequence of k-windows of G contains...

Báo cáo toán học: "List coloring hypergraphs" pdf

... ﬁxed coloring χ of X,P (Bcχ) < 2 exp−|Y |8(8s)s.Since there are at most s|X|colorings o f X, and since by Claim 1 |Y |  pn/2 and |X| 2p2n, the expected number of colorings ... journal of combinatorics 17 (2010), #R129 8 1.1 List coloring graphsThe notion of list -coloring is a generalization of the notion of proper coloring, a nd hasbeen studied extensively for graphs. ... is explicitly displayed.1.2 List coloring hypergraphsThere seem to be very few results on list colorings of hypergraphs. Perhaps the most fa-mous question on colorings of hypergraphs is the...

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