JCT
2007
13 years 4 months ago
2007
It is shown that the coset lattice of a finite group has shellable order complex if and only if the group is complemented. Furthermore, the coset lattice is shown to have a Cohen...
JCT
2007
13 years 4 months ago
2007
A matrix A is said to be partition regular (PR) over a subset S of the positive integers if whenever S is finitely coloured, there exists a vector x, with all elements in the sam...
JCT
2007
13 years 4 months ago
2007
We show that certain modular equations and theta function identities of Ramanujan imply elegant partition identities. Several of the identities are for t-cores. Key Words: partitio...
JCT
2007
13 years 4 months ago
2007
ABSTRACT. We present an extension of the Delsarte linear programming method for spherical codes. For several dimensions it yields improved upper bounds including some new bounds on...
JCT
2007
13 years 4 months ago
2007
We study the spectral radius of connected non-regular graphs. Let λ1(n,Δ) be the maximum spectral radius among all connected non-regular graphs with n vertices and maximum degre...
JCT
2007
13 years 4 months ago
2007
The codegree density γ(F) of an r-graph F is the largest number γ such that there are F-free r-graphs G on n vertices such that every set of r−1 vertices is contained in at le...
JCT
2007
13 years 4 months ago
2007
A brick is a 3-connected graph such that the graph obtained from it by deleting any two distinct vertices has a perfect matching. The importance of bricks stems from the fact that...
JCT
2007
13 years 4 months ago
2007
Let G be a d-regular graph with girth g, and let α be the independence number of G. We show that α(G) ≥ 1 2 1 − (d − 1)−2/(d−2) − (g) n where (g) → 0 as g → ∞,...
JCT
2007
13 years 4 months ago
2007
Let G be a simple graph with n vertices and m edges. Let ω(G) and α(G) be the numbers of vertices of the largest clique and the largest independent set in G, respectively. In th...
JCT
2007
13 years 4 months ago
2007
