97
Voted
DM
2000
15 years 5 days ago
2000
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...
DM
2000
15 years 5 days ago
2000
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...
81
Voted
COMBINATORICA
2004
15 years 6 days ago
2004
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...
93
Voted
ARSCOM
2004
15 years 6 days ago
2004
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...
JCT
2007
15 years 7 days ago
2007
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...
85
Voted
SIAMDM
2008
15 years 8 days ago
2008
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...
104
click to vote
GC
2007
Springer
15 years 8 days ago
2007
Springer
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 ...
87
Voted
JGT
2006
15 years 9 days ago
2006
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...
88
Voted
DM
2007
15 years 9 days ago
2007
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...
JCT
2006
15 years 9 days ago
2006
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