A graph is said to be pancyclic if it contains cycles of every length from its girth to its order inclusive; and a bipartite graph is said to be bipancyclic if it contains cycles of every even length from its girth to its order. The pancyclicity or the bipancyclicity of a given network is an important factor in determining whether the network’s topology can simulate rings of various lengths. An...

Preface Tournaments constitute perhaps the most well-studied class of directed graphs. One of the reasons for the interest in the theory of tournaments is the monograph Topics on Tournaments [58] by Moon published in 1968, covering all results on tournaments known up to this time. In particular, three results deserve special mention: in 1934 Rédei [60] proved that every tournament has a directe...

Diese Dissertation ist auf den Internetseiten der Hochschulbibliothek online verfügbar. Preface Graph theory as a very popular area of discrete mathematics has rapidly been developed over the last couple of decades. Numerous theoretical results and countless applications to practical problems have been discovered. The concepts of k-ordered graphs and out-arc pancyclicity are two recent topics i...

If D is a strongly connected digraph, then an arc set S of D is called a restricted arc-cut of D if D − S has a non-trivial strong component D1 such that D − V (D1) contains an arc. Recently, Volkmann [12] defined the restricted arc-connectivity λ(D) as the minimum cardinality over all restricted arc-cuts S. A strongly connected digraph D is called λconnected when λ(D) exists. Let k ≥ 2 be an i...

If x is a vertex of a digraph D, then we denote by d(x) and d−(x) the outdegree and the indegree of x, respectively. The global irregularity of a digraph D is defined by ig(D) = max{d+(x), d−(x)}−min{d+(y), d−(y)} over all vertices x and y of D (including x = y). If ig(D) = 0, then D is regular and if ig(D) ≤ 1, then D is almost regular. A c-partite tournament is an orientation of a complete c-...

If x is a vertex of a digraph D, then we denote by d(x) and d−(x) the outdegree and the indegree of x, respectively. The global irregularity of a digraph D is defined by ig(D) = max{d+(x), d−(x)}−min{d+(y), d−(y)} over all vertices x and y of D (including x = y). If ig(D) = 0, then D is regular and if ig(D) ≤ 1, then D is almost regular. A c-partite tournament is an orientation of a complete c-...

In this paper we study cycle coverings and 2-factors of a claw-free graph and those of its closure, which has been de ned by the rst author (On a closure concept in claw-free graphs, J. Combinatorial Theory Ser. B 70 (1997) 217{224). For a claw-free graph G and its closure cl(G), we prove (1) V (G) is covered by k cycles in G if and only if V (cl(G)) is covered by k cycles of cl(G), and (2) G h...