Báo cáo toán học: "Explicit Ramsey graphs and orthonormal labelings" pdf
Báo cáo toán học: "Explicit Ramsey graphs and orthonormal labelings" pdf
... is
Ω(m
4/3
).
Here we improve this bound and describe an explicit construction of triangle free graphs with
independence numbers m and Ω(m
3/2
) 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, 19...
Báo cáo toán học: "Explicit Ramsey graphs and Erd˝s distance problems o over finite Euclidean and non-Euclidean spaces" ppt
... Tanaka, Finite Euclidean graphs and Ramanujan
graphs, Discrete Mathematics (to appear).
[9] D. Bauer, J. Vandenheuvel and E. Schmeichel, Toughness and Triangle-Free Graphs,
Journal of Combinatorial ... early version of this manuscript and the referee for
helpful suggestions to improve the presentation of this paper.
References
[1] N. Alon, Explicit Ramsey graphs and orthon...
Báo cáo toán học: "Information flows, graphs and their guessing numbers" pptx
... bits and n output bits, and where the depth of the circuit
is in O(log(n)). For a detailed discussion and further survey of this class of problems and
their link to communication complexity and ... (and this paper provide some evidence of this) progress in under-
standing and bounding guessing numbers for various natural classes of graphs is needed in
order to solve some of the...
Báo cáo toán học: "Double-critical graphs and complete minors" pps
... subset A and B such that
the 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 H
1
and H
2
denote
disjoint ... 10
complete graphs.
2 Notation
All graphs considered in this paper are simple and finite. We let n(G) and m(G) denote
the order and size of a graph G, respectiv...
Báo cáo toán học: "Glossary of Signed and Gain Graphs and Allied Areas" docx
... gain, and biased graphs.
directed graph
digraph
• A digraph is an oriented all-positive ordinary graph. Thus, see both “Graph
Structures” and “Orientation” (of signed, gain, and biased graphs) ... signed
graphs.
There are real, physical spin glasses, but I do not discuss them since they are
not graphs. There are also features of models studied in physics, like randomness
of bond s...
Báo cáo toán học: "ON RAMSEY MINIMAL GRAPHS" doc
... 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 Theory and Applications of Graphs (G.Chartrand, ed.) Wiley (1981) pp.159–168.
[5] S.A.Burr, P.Erd˝os, R.J.Faudree, C.C.Rousseau and R.H.Schelp, Ramsey minima...
Báo cáo toán học: "All Ramsey numbers r(K3, G) for connected graphs of order 9" pps
... edges.
References
[1] S. Brandt, Expanding graphs and Ramsey numbers, submitted.
[2] S. Brandt, G. Brinkmann, T. Harmuth, The generation of maximal
triangle-free graphs, submitted.
[3] G. Brinkmann, All Ramsey numbers ... all Ramsey graphs and all maximal graphs needed to determine
the graphs on 10 vertices with Ramsey number 19 was a bit less than 9 days on a
mixed clust...
Báo cáo toán học: "The cube polynomial and its derivatives: the case of median graphs" pps
... Klavˇzar and R.
ˇ
Skrekovski, On median graphs and median grid graphs, Discrete
Math. 219 (2000) 287–293.
[10] S. Klavˇzar, H. M. Mulder, and R.
ˇ
Skrekovski, An Euler-type formula for median
graphs, ... (Chapman and Hall, New York, 1993).
[7] W. Imrich and S. Klavˇzar, Product Graphs: Structure and Recognition (John
Wiley & Sons, New York, 2000).
[8] W. Imrich, S. Klavˇz...
Báo cáo toán học: "On the Graphs of Hoffman-Singleton and Higman-Sims" docx
... On the Graphs of Hoffman-Singleton and
Higman-Sims
Paul R. Hafner
Department of Mathematics
University of Auckland
Auckland (New Zealand)
hafner@math.auckland.ac.nz
Submitted: Mar ... Then u and u
have the same 3 neighbours in each of C
1
, S, and
C
2
. Moreover, if z ∈ L
1
, then u and z
are adjacent if and only if u
and z are adjacent.
Proof. Let w =(4, 0, 0) and consid...
Báo cáo toán học: "Steiner triple systems and existentially closed graphs" ppsx
... 3-existentially closed block intersection graphs. Both of the STS(13)s and 76
of the 80 STS(15)s violate criterion (iii) and the four other STS(15)s, #1, #2, #3 and
#16 in the standard listing in [17] contain ... evidence suggests that 3-e.c. strongly regular graphs which occur as
the block intersection graphs of Steiner triple systems are a rare and elusive species and
likely...