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DM
2000
158views more  DM 2000»
13 years 3 months ago
Bipartite Ramsey numbers and Zarankiewicz numbers
The Zarankiewicz number z(s, m) is the maximum number of edges in a subgraph of K(s, s) that does not contain K(m, m) as a subgraph. The bipartite Ramsey number b(m, n) is the lea...
Wayne Goddard, Michael A. Henning, Ortrud R. Oelle...
DM
2000
64views more  DM 2000»
13 years 3 months ago
Size functions of subgeometry-closed classes of representable combinatorial geometries
Let exq(G; n) be the maximum number of points in a rank-n geometry (simple matroid) that is representable over GF(q) and that has no restriction isomorphic to the geometry G. We fi...
Joseph E. Bonin, Hongxun Qin
COMBINATORICA
2004
69views more  COMBINATORICA 2004»
13 years 3 months ago
Structural Results For Planar Sets With Many Similar Subsets
Consider a k-element subset P of the plane. It is known that the maximum number of sets similar to P that can be found among n points in the plane is (n2 ) if and only if the cros...
Bernardo M. Ábrego, György Elekes, Sil...
ARSCOM
2004
124views more  ARSCOM 2004»
13 years 3 months ago
The Domatic Number of Regular Graphs
The domatic number of a graph G is the maximum number of dominating sets into which the vertex set of G can be partitioned. We show that the domatic number of a random r-regular g...
Peter Dankelmann, Neil J. Calkin
JCT
2007
82views more  JCT 2007»
13 years 3 months ago
A new generalization of Mantel's theorem to k-graphs
Let the k-graph Fank consist of k edges that pairwise intersect exactly in one vertex x, plus one more edge intersecting each of these edges in a vertex different from x. We prov...
Dhruv Mubayi, Oleg Pikhurko
SIAMDM
2008
154views more  SIAMDM 2008»
13 years 3 months ago
On the First-Fit Chromatic Number of Graphs
The first-fit chromatic number of a graph is the number of colors needed in the worst case of a greedy coloring. It is also called the Grundy number, which is defined to be the max...
József Balogh, Stephen G. Hartke, Qi Liu, G...
GC
2007
Springer
13 years 3 months ago
On the Maximum Number of Cliques in a Graph
A clique is a set of pairwise adjacent vertices in a graph. We determine the maximum number of cliques in a graph for the following graph classes: (1) graphs with n vertices and m ...
David R. Wood
JGT
2006
95views more  JGT 2006»
13 years 3 months ago
Maximal independent sets in graphs with at most r cycles
We find the maximum number of maximal independent sets in two families of graphs. The first family consists of all graphs with n vertices and at most r cycles. The second family i...
Goh Chee Ying, Koh Khee Meng, Bruce E. Sagan, Vinc...
DM
2007
119views more  DM 2007»
13 years 3 months ago
Short proofs for cut-and-paste sorting of permutations
We consider the problem of determining the maximum number of moves required to sort a permutation of [n] using cut-and-paste operations, in which a segment is cut out and then pas...
Daniel W. Cranston, Ivan Hal Sudborough, Douglas B...
JCT
2006
54views more  JCT 2006»
13 years 3 months ago
Matroid packing and covering with circuits through an element
Abstract. In 1981, Seymour proved a conjecture of Welsh that, in a connected matroid M, the sum of the maximum number of disjoint circuits and
Manoel Lemos, James G. Oxley