On a problem of P. Vestergaard concerning circuits in graphs
On a problem of R. Häggkvist concerning edge-colourings of graphs
On a problem of R. Halin concerning subgraphs of infinite graphs
On a problem of R.L.Graham
On a problem of Steinhaus concerning binary sequences.
On a problem of walks
In 1995, F. Jaeger and M.-C. Heydemann began to work on a conjecture on binary operations which are related to homomorphisms of De Bruijn digraphs. For this, they have considered the class of digraphs such that for any integer , has exactly walks of length , where is the order of . Recently, C. Delorme has obtained some results on the original conjecture. The aim of this paper is to recall the conjecture and to report where all the authors arrived.
On a property of neighborhood hypergraphs
The aim of the paper is to show that no simple graph has a proper subgraph with the same neighborhood hypergraph. As a simple consequence of this result we infer that if a clique hypergraph and a hypergraph have the same neighborhood hypergraph and the neighborhood relation in is a subrelation of such a relation in , then is inscribed into (both seen as coverings). In particular, if is also a clique hypergraph, then .
On a quasiordering of bipartite graphs.
On a question of K. Leeb
On a Rado type problem for homogeneous second order linear recurrences.
On a restricted -non-squashing partition function.
On a result of Williamson.
On a septuple product identity.
On a Spanning k-Tree in which Specified Vertices Have Degree Less Than k
A k-tree is a tree with maximum degree at most k. In this paper, we give a degree sum condition for a graph to have a spanning k-tree in which specified vertices have degree less than k. We denote by σk(G) the minimum value of the degree sum of k independent vertices in a graph G. Let k ≥ 3 and s ≥ 0 be integers, and suppose G is a connected graph and σk(G) ≥ |V (G)|+s−1. Then for any s specified vertices, G contains a spanning k-tree in which every specified vertex has degree less than k. The degree...
On a special case of Hadwiger's conjecture
Hadwiger's Conjecture seems difficult to attack, even in the very special case of graphs G of independence number α(G) = 2. We present some results in this special case.
On a sphere of influence graph in a one-dimensional space
A sphere of influence graph generated by a finite population of generated points on the real line by a Poisson process is considered. We determine the expected number and variance of societies formed by population of n points in a one-dimensional space.
On A System Of All Maximal Chains (Antichains) Of A Graph
On a technique for representing semigroups as endomorphism semigroups of graphs with given property.
On a theorem of Erdős, Rubin, and Taylor on choosability of complete bipartite graphs.
On a theorem of Fröberg and saturated graphs.