James B. Shearer

A new table of constant weight codes

A table of binary constant weight codes of length nl28 is presented. Explicit constructions are given for most of the 600 codes in the table; the majority of these codes are new. The known techniques for constructing constant weight codes are surveyed, and a table of (unrestricted) binary codes of length nl28 is given

A note on the independence number of triangle-free graphs

Let G be a triangle-free graph on n points with average degree d. Let @a be the independence number of G. In this note we give a simple proof that @a >= n (d ln d - d + 1)/(d - 1)^2. We also consider what happens when G contains a limited number of triangles.

On a problem of Spencer

AbstractLetX1, ...,Xn be events in a probability space. Let ϱi be the probabilityXi occurs. Let ϱ be the probability that none of theXi occur. LetG be a graph on [n] so that for 1 ≦i≦n Xi is independent of ≈Xj‖(i, j)∉G≈. Letf(d) be the sup of thosex such that if ϱ1, ..., ϱn≦x andG has maximum degree ≦d then ϱ>0. We showf(1)=1/2,f(d)=(d−1)d−1d−d ford≧2. Hence

Note on the independence number of triangle-free graphs, II

\mathop {\lim }\limits_{d \to \infty }

A Property of Euclid’s Algorithm and an Application to Padé Approximation

df(d)=1/e. This answers a question posed by Spencer in [2]. We also find a sharp bound for ϱ in terms of the ϱi andG.

Random Walks on Regular and Irregular Graphs

A board

On the independence number of sparse graphs

\mathcal{B}

On the distribution of the maximum eigenvalue of graphs

is a finite set of unit squares lying in the plane whose corners have integer coordinates. A rectangle of