
A known theorem of Bigalke and Jung says that the only nonhamiltonian, tough graph
Given a sequence
Let
for any pair
A series of partially balanced incomplete block design yields under certain
restrictions, a new series of BIB designs with parameters:
where
A
In this note we introduce a lemma which is useful in studying the chromaticity of graphs. As examples, we give a short proof for a conclusion in
The existence of difference sets in abelian
We deal with conditions on the number of arcs sufficient for bipartite digraphs to have cycles and paths with specified properties.
The convex hull of graph
In the paper, the maximum number of corners of the convex hull of an
Conjectured generalizations of Hadwiger’s Conjecture are discussed. Among other results, it is proved that if
In 1967 Alspach [1] proved that every arc of a diregular tournament is contained in cycles of all possible lengths. In this paper, we extend this result to bipartite tournaments by showing that every arc of a diregular bipartite tournament is contained in cycles of all possible even lengths, unless it is isomorphic to one of the graphs
In this paper we study the edge clique graph
In this paper we construct pairwise balanced designs (PBDs) having block sizes which are prime powers congruent to
A Nuclear Design
A graph
In “On the exact minimal (1, 4)-cover of twelve points” (\textit{Ars Combinatoria} 27, 3–18, 1989), Sane proved that if
It is shown that a
We give a construction of a row-complete Latin square, which cannot be made column-complete by a suitable permutation of its rows, for every even order greater than
In a recent paper, Gustavus J. Simmons introduced a new class of combinatorial-geometric objects he called “campaign graphs”. A
The main aim of this note is to show that Simmons’ result holds for
Let
We show that for all odd
Given an overlarge set of Steiner triple systems, each on
Halberstam, Hoffman and Richter introduced the idea of a Latin triangle as an analogue of a Latin square, showed the existence or non-existence of Latin triangles for small orders, and used a multiplication technique to generate triangles of orders
A graph covering projection is a local graph homeomorphism. Certain partitions of the vertex set of the preimage graph induce a notion of “concreteness”. The concrete graph covering projections will be counted up to isomorphism.
The set of all distinct blocks of a
The cycle graph
A Latin square of order
Let
Golomb and Taylor (joined later by Etzion) have modified the notion of a complete Latin square to that of a Tuscan-
It is shown that if
Let the edges of the complete graph
Uniquely pseudointersectable graphs are defined; this is closely related to the uniquely intersectable graphs introduced by Alter and Wang [1]. The S-property is necessary but not sufficient for a graph to be uniquely pseudointersectable. This condition is also sufficient for graphs with unique minimum cover. Finally, we show that for supercompact graphs, unique pseudointersectability and unique intersectability are equivalent. Thus we generalize some of the results in [1] to a wider class of graphs.
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