Báo cáo toán học: "On-line list colouring of graphs" pot
Báo cáo toán học: "Game list colouring of graphs" ppt
... wins if and only if in the process of the game list colouring Bob first colours a vertex of C4.Lemma 5 Let L be a 2 -list- assignment of C4, other than the lists in Figure 4 and Fig-ure 5. ... process of the game list colouring a graph G is par-tially coloured. If all uncoloured vertices of G are safe then Alice wins.Now we will consider a game list colouring but with the first move of ... containk+12elements of C1andk+12elements of C2. If k + 1 is odd, each of the selected (k + 1)-subsets will containk2+ 1elements of C1andk2elements of C2. Assign each of these (k + 1)-subsets of...
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Báo cáo toán học: "The independence number of graphs with large odd girth" ppt
... independence number of general graphs of a given odd girth. We shall prove some similar bounds tothose we prove for regular graphs in terms of a measure of the concentration of edges.Monien and ... for the independencenumber in terms of the odd girth, but instead of the average degree of the graphwe have to use another measure of the concentration of edges.8References[1] Ajtai, M.,Koml´os, ... remarksA vertex cover of a graph G is a set of vertices U so that for every edge ab ∈ E(G)a or b is a member of U . We shall write λ(G) for the minimum size of a vertexcover of G.The vertex cover...
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Báo cáo toán học: "On the connectivity of graphs embedded in surfaces II" docx
... [γ(Km)+1,gA−1], none of the genera admits the genus embedding of anythe electronic journal of combinatorics 9 (2002), #R38 25construction of graph HIB(s, k, l) up through the selection of faces F1through ... l)) = 2l +3.Proof: The proof proceeds just as in the proof of Theorem 3.2. For Part (i), theonly difference is that here for HIB(s, k, l) we have deleted one edge from each of Ψ andΨ, but ... each of these cases, the addition of two extra edgeson one of the connecting tubes suffices to attain the genus bound in Lemma 3.1.Now in all twelve cases (for each of the twelve values of k)...
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Báo cáo toán học: "The Insertion Encoding of Permutations" pot
... similar to that of Theorem 2 in Section 2 of [2]. Its proofis identical to the proof of that theorem, and depends only on the following modification of Proposition 5 from the same section of that paper.Lemma ... insertions of any type provided only that they canbe followed by further insertions leading to an element of L. The number of elements of L of length n is then just the number of walks in Gn of length ... 1 elements of π so that one of them is placed intoeach of the slots of this configuration. These 2k + 1 elements witness the involvement inπ of one of the permutations in S2k+1 of the form...
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Báo cáo toán học: "a matrix representation of graphs and its spectrum as a graph invariant" ppt
... SeveriniDepartment of Mathematics and Department of Computer ScienceUniversity of York, York YO10 5DD, U.K.ss54@york.ac.ukRichard C. WilsonDepartment of Computer ScienceUniversity of York, York ... Wedescribe some structural properties of the digraph D obtained from U3.InSection4,we list the sets of strongly regular graphs for which the eigenvalues of D successfully distin-guish a graph ... forsome p, is presumably different from the support of M(−→LDG)p. This is because of thecontribution of the negative entries in U(G). On the basis of this observation, we definethe following matrix.Definition...
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Báo cáo toán học: " Reduced Canonical Forms of Stoppers" pot
... journal of combinatorics 13 (2006), #R57 6Proof of Lemma 2.9. Let α −β be a follower of γ −δ.Wesaythatα−β is safe if Left cansurvive both α − H and H − β moving second, for some follower H of G. ... + over modulo Inf.The importance of this observation stems from the fact that S contains a great manyidempotents. Several of these are listed in Figure 8 of [10]. A typical example isn= {0||0, ... class of loopy games knownas stoppers.The arsenal of tools available in the study of loopy games is currently rather lim-ited. The temperature theory and the theory of atomic weights, two of...
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Báo cáo toán học: "On (δ, χ)-bounded families of graphs" ppsx
... no vertex of T0is adjacent toany vertex of L. The distance of any vertex in T0from the farthest vertex in C is at mostr + i/2. The distance of any vertex in the previous copies of Trpin ... journal of combinatorics 18 (2011), #P108 3 of degree one and let v be any such vertex of G. Set G′= G \ v. We may assume thatH contains an induced copy of G′. Denote this copy of G′in ... the order of G. If G consists of only a cycle then its length is i and anysmallest cycle of H is isomorphic to G. Assume now that G contains at least one vertexthe electronic journal of combinatorics...
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Báo cáo toán học: "total weight choosability of graphs" pptx
... new collection L of lists of size 2 for G= (V, E) inthe following way. The lists of the edges do not change (except for the fact that there are(n − 1) less of such lists). For each ... 05C78AbstractSuppose the edges and the vertices of a simple graph G are assigned k-elementlists of real weights. By choosing a representative of each list, we specify a vertex colouring, where for each vertex ... edge set of a graph G, and assume we are given a collection L = {Lv1, . . . , Lvn, Le1, . . . ,Lem} of lists of size k assigned to the vertices and the edges of G. For each list La∈...
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Báo cáo toán học: "Perfect matchings in -regular graphs" potx
... proved by Br´egman [2] (c.f. also [1] for a probabilisticdescription of a proof of Schrijver). Indeed, the Minc conjecture states that thepermanent of an n by n matrix A with (0, 1) entries satisfiesper(A) ... The solution of the van der Waerden problem for permanents,Dokl. Akad. Nauk SSSR 258 (1981), 1041-1044.[4] D. I. Falikman, A proof of van der Waerden’s conjecture on the permanent of adoubly ... >d>2>0andn>n0(), the number of perfect matchingsin any such graph is at least (d − 2)nn! and at most (d +2)nn!. The proofrelies on the validity of two well known conjectures for...
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Báo cáo toán học: "On k-Ordered Bipartite Graphs" potx
... journal of combinatorics 10 (2003), #R11 10Proof: Let S = {x1,x2, ··· ,xk} be an ordered subset of the vertices of G.LetCbe a cycle of maximum order 2c containing all vertices of S in ... contradiction to the above inequality.Let c be the number of elements of S that are not vertices on any of the k + t edges of the matching. Then t + d + c of the edges are free. We are now prepared to construct ... of the intervals of C determined by S,say[xi,xi+1]. Let z1and z2be the immediatesuccessor and predecessor on C to the neighbors of x and y respectively according to theorientation of...
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