COMBINATORICS
2007
13 years 4 months ago
2007
COMBINATORICS
2007
13 years 4 months ago
2007
Let G = (V, E) be any d-regular graph with girth g on n vertices, for d ≥ 3. This note shows that G has a maximum matching which includes all but an exponentially small fraction...
COMBINATORICS
2007
13 years 4 months ago
2007
This paper deals with new infinite families of small dense sets in desarguesian projective planes PG(2, q). A general construction of dense sets of size about 3q2/3 is presented....
COMBINATORICS
2007
13 years 4 months ago
2007
We prove that if G is a graph containing a doubly-critical edge and satisfying χ ≥ ∆ ≥ 6, then G contains a K∆.
COMBINATORICS
2007
13 years 4 months ago
2007
Let λ be a partition, and denote by fλ the number of standard tableaux of shape λ. The asymptotic shape of λ maximizing fλ was determined in the classical work of Logan and S...
COMBINATORICS
2007
13 years 4 months ago
2007
We derive several interesting formulae for the eigenvalues of the derangement graph and use them to settle affirmatively a conjecture of Ku regarding the least eigenvalue.
COMBINATORICS
2007
13 years 4 months ago
2007
We compute the spectrum of the Schreier graph of the symmetric group Sn corresponding to the Young subgroup S2 × Sn−2 and the generating set consisting of initial reversals. In ...
COMBINATORICS
2007
13 years 4 months ago
2007
Let µ (G) and µmin (G) be the largest and smallest eigenvalues of the adjacency matrix of a graph G. Our main results are: (i) If H is a proper subgraph of a connected graph G o...
COMBINATORICS
2007
13 years 4 months ago
2007
COMBINATORICS
2007
13 years 4 months ago
2007
The dartboard problem is to arrange n numbers on a circle to obtain maximum risk, which is the sum of the q-th power of the absolute differences of adjacent