Báo cáo toán học: "Information ﬂows, graphs and their guessing numbers" pptx

Báo cáo toán học: "Glossary of Signed and Gain Graphs and Allied Areas" docx

... class (of signed, gain, or bidirected graphs) Notation: [], [], [B]ã An equivalence class of signed, gain, or bidirected graphs under switching. 27isomorphism (of signed, gain, or bidirected graphs) Notation:=ã ... signing of the underlying graph. Equiva-lent to being additively biased. signed gain graph signed graph with gainsNotation: (Γ,σ,ϕ), (Φ,σ), (,)ã A graph separately gained and signed. signed and ... 13sign of a polygon (in a signed graph) gain of a polygon (in a gain graph)Notation: (C), (C)ã The product of the signs, or gains (taken in the order and direction of an ori-entation of the...

Báo cáo toán học: "Explicit Ramsey graphs and orthonormal labelings" pdf

... isΩ(m4/3).Here we improve this bound and describe an explicit construction of triangle free graphs withindependence numbers m and Ω(m3/2) vertices. Our graphs are Cayley graphs and their construc-tion ... Tough Ramsey graphs without short cycles, to appear.[3] N. Alon and N. Kahale, in preparation.[4] N. Alon and J. H. Spencer, The Probabilistic Method, Wiley, 1991.[5] F.R.K.Chung,R.CleveandP.Dagum,A ... Mathematics (AMS 1983), 67-70.[10] J. H. Kim, The Ramsey number R(3,t) has order of magnitude t2/ log t, to appear. Explicit Ramsey graphs and orthonormal labelingsNoga Alon∗Submitted: August...

Báo cáo toán học: "TIGHT UPPER BOUNDS FOR THE DOMINATION NUMBERS OF GRAPHS WITH GIVEN ORDER AND MINIMUM DEGREE" pdf

... δ). We establish these values inSections 2, 3 and 4. TIGHT UPPER BOUNDS FOR THE DOMINATION NUMBERS OF GRAPHS WITH GIVEN ORDER AND MINIMUM DEGREEW. Edwin ClarkUniversity of South FloridaTampa, ... y.IfA⊆V then we let A denote the subgraph of G induced by A.Table 1 contains the value of γ(n, δ) for n ≤ 16, 0 ≤ δ ≤ n − 1 if the value isknown, otherwise upper and lower bounds for γ(n, ... be the 8-cycle with 4 diameters added, and G10= G4∪ G6. This leaves only G9 and G11. See appendix B for these graphs, namely the graphs listed there as G(9 3 3) and G(11 3 4)  the...

Báo cáo toán học: "Tight Upper Bounds for the Domination Numbers of Graphs with Given Order and Minimum Degree, II." pdf

... graph of order n with domination number at least 3 and minimum degree δ satisfyingn −2√n −4 ≤ δ ≤ n −√2√n. Tight Upper Bounds for the Domination Numbers of Graphs with Given Order and Minimum ... combinatorics 7 (2000), #R58 19[2] W. Edwin Clark and Larry A. Dunning, Tight Upper Bounds for the Domination Numbers of Graphs with Given Order and Minimum Degree, Electron. J. Combin.4 (1997), no. ... in the case of δ3(n). For thisit is useful to ﬁnd circulant graphs of order n with large minimum degree and with domination number at least 3. This turns out to be related to the existence of...

Báo cáo toán học: "On the upper and lower chromatic numbers of BSQSs(16)" ppt

... coloureddiﬀerently. The upper and lower chromatic numbers ¯χ, χ are the maximum and minimum numbers of colours for which there exists a colouring using all the colours. The concepts of mixed hypergraph, upper and ... =3or χ =2. the electronic journal of combinatorics 8 (2001), #R6 7 On the upper and lower chromatic numbers of BSQSs(16)∗Giovanni Lo FaroDepartment of Mathematics, University of MessinaSalita ... ¯χ =3. The next theorem completes theorem 3 and gives important information about the chro-matic spectrum of BSQSs(16).Theorem 4 The upper chromatic number for all BSQSs(16)is¯χ =3; the lower...

Báo cáo toán học: "The cube polynomial and its derivatives: the case of median graphs" pps

... . the electronic journal of combinatorics 10 (2003), #R3 5 Proof. The proof is by induction on the number of vertices of a graph. The n -cube Qn,n ≥ 1, can be obtained as the expansion of the ... graphs Ue and derivec(s+1)(G, −1) =e∈F(G)θs(Ue)=θs+1(G). the electronic journal of combinatorics 10 (2003), #R3 8 The cube polynomial and its derivatives: the case of median graphsBoˇstjan ... properties, is up to the factor f(Q0,x) the cube polynomial. The derivation ∂G of a median graph G isintroduced and it is proved that the cube polynomial is the only function f with the property f(G,...

Báo cáo toán học: "On the Graphs of Hoﬀman-Singleton and Higman-Sims" docx

... same family of maximum cocliques of X and hence there exists an automorphism of Z mapping X to Y .Proof. The statement of the lemma gives sufficient indication of the proof. We note that the lemma ... The subgraph of order 80 induced by four of these subgraphs Wiis identifiedas the second orbit of the stabiliser of the remaining one of these graphs in [4]. What isnew here is the observation ... toone of the HS-orbits, rows 3 and 4 to the other. The last row lists the number of Hoffman-Singleton graphs with each intersection pattern above it. It is evident thatmembers X of the HS-orbit of...

Báo cáo toán học: "Steiner triple systems and existentially closed graphs" ppsx

... an n -existentially closed graph is (n − 1) -existentially closed, the theoremis trivially true for v = 7 and 9. There are two non-isomorphic STS(13)s and 80 non-isomorphic STS(15)s, [17], and ... systems and conﬁgurations.2 Steiner triple systems A Steiner triple system of order v, STS(v), is a pair (V, B) where V is a set of cardinalityv of elements, or points, and B is a collection of triples, ... electronic journal of combinatorics 12 (2005), #R42 12 Steiner triple systems and existentially closed graphsA.D. Forbes, M.J. Grannell and T.S. GriggsDepartment of Pure MathematicsThe Open UniversityWalton...

Báo cáo toán học: "Decompositions of graphs into 5-cycles and other small graphs" ppsx

... Decompositions of graphs into 5-cycles and other small graphs Teresa Sousa∗Tepper School of BusinessCarnegie Mellon UniversityPittsburgh, PA 15213tmj@andrew.cmu.eduSubmitted: ... non-complete graphs of order 4 and single edges. Let H be one of the following graphs. Theorem 2.4. Any graph of order n,withn ≥ 4, can be decomposed into at most n24copies of H and single ... edge of G is an edge of exactly one of G1, ,Gt and allG1, ,Gt∈ .Letφ(G, ) denote the minimum size of an -decomposition of G. The main problem related to-decompositions is the one of ﬁnding...

Báo cáo toán học: "Fractional biclique covers and partitions of graphs" ppsx

... one of thebicliques in B.Thebiclique cover number, bc(G), of a graph G is the minimum number of bicliques in a biclique cover of G.Abiclique partition of a graph G is a collection B of bicliques ... above and the other is K(RGì SH,SGì RH). A biclique of G ì Hwhich is one of the two bicliques produced from the weak product of a biclique of G and a biclique of H is called a product biclique ... ordered bicliques of G and H, respectively, for (3). Construct a weighting w of the ordered bicliques of GìHfrom the ordered bicliques of G and H.IfB is an ordered product biclique of GìH and B...

Báo cáo toán học: "The spectral radius and the maximum degree of irregular graphs" doc

... spectral radius of a general (not necessarily regular)graph G and that of a subgraph of G, see [16].2 The spectral radius and the maximum degree The following theorem is the main result of this ... to the extreme entries of the principal eigenvector of an irregular graph G, then one can improve the result of Theorem 2.1. However, thereare infinite families of irregular graphs for which the ... analyze the effect of adding an edge on the spectral radius of a regulargraph. We need different techniques in this case because the spectral radius will be closerto the minimum degree than to the maximum...

Báo cáo toán học: "Information ﬂows, graphs and their guessing numbers" pptx

... d(Gπ, s) ≥ n − k(G, s) and therefore d(Gπ, s) > n/2 forn ≥ 4d2(4d + 3). ♣the electronic journal of combinatorics 14 (2007), #R44 16 Information ﬂows, graphs and their guessing numbersSøren ... bits and n output bits, and where the depth of the circuitis in O(log(n)). For a detailed discussion and further survey of this class of problems and their link to communication complexity and ... concerning guessing numbers.In my judgement (and this paper provide some evidence of this) progress in under-standing and bounding guessing numbers for various natural classes of graphs is needed...

Báo cáo toán học: "Explicit Ramsey graphs and Erd˝s distance problems o over ﬁnite Euclidean and non-Euclidean spaces" ppt

... Section 2 we construct our main toolsto 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 ofnon-isotropic points. Similar results hold for ... action of simple orthogonal group O ±2m(q) (qodd) on the set of non-isotropic pointsLet V =2mqbe the 2m-dimensional vector space over the finite fieldq(q is an odd primepower). For each...

Báo cáo toán học: "Double-critical graphs and complete minors" pps

... 10 complete graphs. 2 NotationAll graphs considered in this paper are simple and ﬁnite. We let n(G) and m(G) denotethe order and size of a graph G, respectively. The path, the cycle and the complete ... subset A and B such thatthe induced graphs G[A] and G[B] are edge-empty and complete, respectively, and, thus,we have a contradiction by Proposition 5.1. Suppose |S|  4, and let H1 and H2denotedisjoint ... constructed by taking the complete (k − 6)-graph and two copies of an oddcycle Cℓwith ℓ  5 and joining these three graphs completely. Then the non -complete graph Hk,ℓis k-critical, and the ratio of...

Báo cáo toán học: "Thin Lehman Matrices and Their Graphs" docx

... Lehman matrices are the thin Lehman matrices and the point-line incidence matrices of nondegenerate finite projective planes. We wouldlike to know if there are any other infinite families of Lehman ... finite nondegenerate projective planes, a widely studiedtopic [4], and thin Lehman matrices. Thin Lehman matrices were defined and studied byCornuéjols et al. [3].the electronic journal of combinatorics ... problemsThe classification of Lehman matrices, or even only thin Lehman matrices, is still anopen problem. We have used the Johnson subgraph to give structural results for thin Lehman matrices, which we...

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