On the number of cycles in a graph
Frank Harary, Bennet Manvel (1971)
Matematický časopis
Mašulović, Dragan (1998)
Novi Sad Journal of Mathematics
Legendre, Stéphane, Paclet, Philippe (2011)
Journal of Integer Sequences [electronic only]
Angelini, Patrizio, Cittadini, Luca, Didimo, Walter, Frati, Fabrizio, Di Battista, Giuseppe, Kaufmann, Michael, Symvonis, Antonios (2011)
Journal of Graph Algorithms and Applications
Amplify Sawkmie, Madan Mohan Singh (2015)
Czechoslovak Mathematical Journal
For any two positive integers and , let be a digraph whose set of vertices is and such that there is a directed edge from a vertex to a vertex if . Let be the prime factorization of . Let be the set of all primes dividing and let be such that and . A fundamental constituent of , denoted by , is a subdigraph of induced on the set of vertices which are multiples of and are relatively prime to all primes . L. Somer and M. Křížek proved that the trees attached to all cycle...
Michael Andresen (2009)
Discussiones Mathematicae Graph Theory
A comparability graph is a graph whose edges can be oriented transitively. Given a comparability graph G = (V,E) and an arbitrary edge ê∈ E we explore the question whether the graph G-ê, obtained by removing the undirected edge ê, is a comparability graph as well. We define a new substructure of implication classes and present a complete mathematical characterization of all those edges.
Jozef Bucko, Peter Mihók (2006)
Discussiones Mathematicae Graph Theory
We introduce object systems as a common generalization of graphs, hypergraphs, digraphs and relational structures. Let C be a concrete category, a simple object system over C is an ordered pair S = (V,E), where E = A₁,A₂,...,Aₘ is a finite set of the objects of C, such that the ground-set of each object is a finite set with at least two elements and . To generalize the results on graph colourings to simple object systems we define, analogously as for graphs, that an additive induced-hereditary...
Alfonz Haviar, Gabriela Monoszová (2001)
Discussiones Mathematicae Graph Theory
In this paper we investigate varieties of orgraphs (that is, oriented graphs) as classes of orgraphs closed under isomorphic images, suborgraph identifications and induced suborgraphs, and we study the lattice of varieties of tournament-free orgraphs.
González, L., Ordaz, O., Quiroz, D. (2008)
Divulgaciones Matemáticas
Futaba Okamoto, Ping Zhang, Varaporn Saenpholphat (2007)
Mathematica Bohemica
Let be an oriented graph of order and size . A -labeling of is a one-to-one function that induces a labeling of the arcs of defined by for each arc of . The value of a -labeling is A -labeling of is balanced if the value of is 0. An oriented graph is balanced if has a balanced labeling. A graph is orientably balanced if has a balanced orientation. It is shown that a connected graph of order is orientably balanced unless is a tree, , and every vertex of...
Jaroslav Ježek (2004)
Czechoslovak Mathematical Journal
We investigate congruences in one-element extensions of algebras in the variety generated by tournaments.
Jürgen Eufinger (1971)
Journal für die reine und angewandte Mathematik
Maciej M. Syslo (1981)
RAIRO - Operations Research - Recherche Opérationnelle
M.von Golitschek (1982)
Numerische Mathematik
Aguiló, F., Simó, E., Zaragozá, M. (2003)
The Electronic Journal of Combinatorics [electronic only]
J.-C. Bermond (1972)
Mathématiques et Sciences Humaines
Irène Charon, Olivier Hudry, Frédéric Woirgard (1996)
Mathématiques et Sciences Humaines
Dans cet article, nous essayons de faire le point sur les résultats concernant les aspects combinatoires et algorithmiques des ordres médians et des ordres de Slater des tournois. La plupart des résultats recensés sont tirés de différentes publications ; plusieurs sont originaux.
Wayne Goddard, Kiran Kanakadandi (2007)
Discussiones Mathematicae Graph Theory
The orientation distance graph 𝓓ₒ(G) of a graph G is defined as the graph whose vertex set is the pair-wise non-isomorphic orientations of G, and two orientations are adjacent iff the reversal of one edge in one orientation produces the other. Orientation distance graphs was introduced by Chartrand et al. in 2001. We provide new results about orientation distance graphs and simpler proofs to existing results, especially with regards to the bipartiteness of orientation distance graphs and the representation...
Vincent Chouinard-Prévost, Alexandre Côté, Claude Tardif (2004)
Commentationes Mathematicae Universitatis Carolinae
We provide the list of all paths with at most arcs with the property that if a graph admits an orientation such that one of the paths in our list admits no homomorphism to , then is -colourable.
N.R. Aravind, N. Narayanan, C.R. Subramanian (2011)
Discussiones Mathematicae Graph Theory
We obtain some improved upper and lower bounds on the oriented chromatic number for different classes of products of graphs.