Neighbourhood digraphs
Neighbourhood tournaments
New classes of critical kernel-imperfect digraphs
A kernel of a digraph D is a subset N ⊆ V(D) which is both independent and absorbing. When every induced subdigraph of D has a kernel, the digraph D is said to be kernel-perfect. We say that D is a critical kernel-imperfect digraph if D does not have a kernel but every proper induced subdigraph of D does have at least one. Although many classes of critical kernel-imperfect-digraphs have been constructed, all of them are digraphs such that the block-cutpoint tree of its asymmetrical part is a path....
New graphs of finite mutation type.
New proofs of the uniqueness of extremal noneven digraphs.
n-Functional digraphs uniquely determined by the skeleton
We show that any total n-functional digraph D is uniquely determined by its skeleton up to the orientation of some cycles and infinite chains. Next, we characterize all graphs G such that each n-functional digraph obtained from G by directing all its edges is total. Finally, we describe finite graphs whose edges can be directed to form a total n-functional digraph without cycles.
n-functionality of graphs
We first characterize in a simple combinatorial way all finite graphs whose edges can be directed to form an n-functional digraph, for a fixed positive integer n. Next, we prove that the possibility of directing the edges of an infinite graph to form an n-functional digraph depends on its finite subgraphs only. These results generalize Ore's result for functional digraphs.
Nombre de sauts et graphes série-parallèles
Nombre maximum d’ordres de Slater des tournois vérifiant
On s’intéresse ici au nombre maximum d’ordres de Slater qu’admettent les tournois vérifiant , où est un paramètre calculé à partir des scores de . On détermine ce nombre maximum d’ordres de Slater, de l’ordre de , si désigne le nombre de sommets. On donne de plus la forme des tournois vérifiant et maximisant le nombre d’ordres de Slater. En particulier, on obtient que ces tournois ne sont pas fortement connexes pour pair.
Nonderogatory unicyclic digraphs.
Nonexistence of almost Moore digraphs of diameter three.
Note on the regular digraphs
Note on the relation between radius and diameter of a graph
The known relation between the standard radius and diameter holds for graphs, but not for digraphs. We show that no upper estimation is possible for digraphs. We also give some remarks on distances, which are either metric or non-metric.
Notes on sufficient conditions for a graph to be hamiltonian.
Nowhere-zero 3-flows in squares of graphs.
On (4, 2)-digraphs containing a cycle of length 2.
On a certain class of multidigraphs, for which reversal of no arc decreases the number of their cycles
On a certain numbering of the vertices of a hypergraph
On a classification of Hamiltonian tournaments
On a conjecture by Nash-Williams