
The present paper studies bisectable trees, i.e., trees whose edges can be colored by two colors so that the induced monochromatic subgraphs are isomorphic. It is proved that the number of edges that have to be removed from a tree with maximum degree three to make it bisectable can be bounded by an absolute constant.
We study the maximal intersection number of known Steiner systems and designs obtained from codes. By using a theorem of Driessen, together with some new observations, we obtain many new designs.
Taking as blocks some subspace pairs in a finite unitary geometry, we construct a number of new Balanced Incomplete Block (BIB) designs and Partially Balanced Incomplete Block (PBIB) designs, and also give their parameters.
The support size of a factorization is the sum over the factors of the number of distinct edges in each factor. The spectrum of support sizes of
Latin interchanges have been used to establish the existence of critical sets in Latin squares, to search for subsquare-free Latin squares, and to investigate the intersection sizes of Latin squares. Donald Keedwell was the first to study Latin interchanges in their
own right. This paper builds on Keedwell’s work and proves new results about the existence of Latin interchanges.
A balanced ternary design of order nine with block size three, index two, and
determine that there are exactly
A graph
on
We consider the problem of constructing pairwise balanced designs of order
All non-Hamiltonian cubic
We deal with finite graphs which admit a labeling of edges by pairwise different positive integers from the set
Kibler, Baumert, Lander, and Kopilovich (cf. [7], [1], [10], and [8] respectively), studied the existence of
respectively. Jungnickel (cf. [9]) lists some unsolved problems on difference sets. One of them is to extend Lander’s table somewhat. By following this idea, this paper deals with the existence or non-existence of
It is shown how any integral monoid can be represented as the projection of the intersection of the solution set of a finite collection of linear inequalities, and a lattice, both in a possibly higher dimension. This in turn can be used to derive a known representation using Chvátal functions, in the same dimension as the monoid. Both representations can be regarded as discrete analogues of the classical theorems of Weyl and Minkowski, but applicable in non-polyhedral monoids.
Both the bandwidth and additive bandwidth of a graph supply information about the storage requirements of a representation of the graph. In particular, the bandwidth measures how far
A star-factor of a graph
Let
for each
A holey perfect Mendelsohn design of type
which are disjoint and spanning, that is
Much of chordal graph theory and its applications is based on chordal graphs being the intersection graphs of subtrees of trees. This suggests also looking at intersection graphs of subgraphs of chordal graphs, and so on, with appropriate conditions imposed on the subgraphs.
This paper investigates such a hierarchy of generalizations of “chordal-type” graphs, emphasizing the so-called “ekachordal graphs” — those next in line beyond chordal
graphs. Parts of the theory of chordal graphs do carry over to chordal-type graphs, including a recursive, elimination characterization for ekachordal graphs.
We present a new construction to obtain frames with block size four using certain skew Room frames. The existence results of Rees and Stinson for frames with block size four are improved, especially nfor hole sizes divisible by
frames we construct, we are also able to show that a resolvable
It has been proved that the smallest rectangular board on which a
1970-2025 CP (Manitoba, Canada) unless otherwise stated.