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Antichains in the homomorphism order of graphs

Dwight Duffus, Peter, L. Erdös, Jaroslav Nešetřil, Lajos Soukup (2007)

Commentationes Mathematicae Universitatis Carolinae

Let 𝔾 and 𝔻 , respectively, denote the partially ordered sets of homomorphism classes of finite undirected and directed graphs, respectively, both ordered by the homomorphism relation. Order theoretic properties of both have been studied extensively, and have interesting connections to familiar graph properties and parameters. In particular, the notion of a duality is closely related to the idea of splitting a maximal antichain. We construct both splitting and non-splitting infinite maximal antichains...

Antidomatic number of a graph

Bohdan Zelinka (1997)

Archivum Mathematicum

A subset D of the vertex set V ( G ) of a graph G is called dominating in G , if for each x V ( G ) - D there exists y D adjacent to x . An antidomatic partition of G is a partition of V ( G ) , none of whose classes is a dominating set in G . The minimum number of classes of an antidomatic partition of G is the number d ¯ ( G ) of G . Its properties are studied.

Antiflows, oriented and strong oriented colorings of graphs

Robert Šámal (2004)

Archivum Mathematicum

We present an overview of the theory of nowhere zero flows, in particular the duality of flows and colorings, and the extension to antiflows and strong oriented colorings. As the main result, we find the asymptotic relation between oriented and strong oriented chromatic number.

Antisymmetric flows and strong colourings of oriented graphs

J. Nešetřill, André Raspaud (1999)

Annales de l'institut Fourier

The homomorphisms of oriented or undirected graphs, the oriented chromatic number, the relationship between acyclic colouring number and oriented chromatic number, have been recently intensely studied. For the purpose of duality, we define the notions of strong-oriented colouring and antisymmetric-flow. An antisymmetric-flow is a flow with values in an additive abelian group which uses no opposite elements of the group. We prove that the strong-oriented chromatic number χ s (as the modular version...

Applications harmoniques entre graphes finis et un théorème de superrigidité

Édouard Lebeau (1996)

Annales de l'institut Fourier

Nous définissons une ntoion d’énergie pour des applications entre deux graphes métriques finis et cherchons à minimiser l’énergie au sein d’une classe d’homotopie. Nous démontrons des théorèmes d’existence et d’unicité analogues à ceux de Eells-Sampson et de Hartman pour les applications harmoniques à valeurs dans les variétés à courbure négative ou nulle. Nous montrons également une propriété de stabilité des applications minimisantes par rapport aux revêtements de degré fini à la source. Une application...

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