Motivated by non-local games and quantum coloring problems, we introduce a graph homomorphism game between graphs classical graphs. This is naturally cast as “quantum–classical game,” that is, of two players involving questions answers. generalizes the We show winning strategies in various models for an analog notion non-commutative homomorphisms due to Stahlke [IEEE Trans. Inf. Theory 62(1), 5...

We show that certain canonical realizations of the complexes Hom(G,H) and Hom+(G,H) of (partial) graph homomorphisms studied by Babson and Kozlov are in fact instances of the polyhedral Cayley trick. For G a complete graph, we then characterize when a canonical projection of these complexes is itself again a complex, and exhibit several well-known objects that arise as cells or subcomplexes of ...

We study generalizations of the “contraction-deletion” relation of the Tutte polynomial, and other similar simple operations, to other graph parameters. The question can be set in the framework of graph algebras introduced by Freedman, Lovász and Schrijver in [2], and it relates to their behavior under basic graph operations like contraction and subdivision. Graph algebras were introduced in [2...

We consider four different models of process interactions that unify and generalise models introduced and studied by Angluin et al. [AAD04] and models introduced and studied by Mazurkiewicz [Maz04a,Maz04b]. We encode these models by labelled (hyper)graphs and relabelling rules on this labelled (hyper)graphs called negotiations. Then for these models, we give complete characterisations of labell...

We study generalizations of the " contraction-deletion " relation of the Tutte polynomial, and other similar simple operations, to other graph parameters. The question can be set in the framework of graph algebras introduced by Freedman, Lovász and Schrijver in [2], and it relates to their behavior under basic graph operations like contraction and subdivision. Graph algebras were introduced in ...

The chromatic sum Σ(G) of a graph G is the smallest sum of colors among of proper coloring with the natural number. In this paper, we introduce a necessary condition for the existence of graph homomorphisms. Also, we present Σ(G) < χf (G)|G| for every graph G.

Bounds on the range of random graph homomorphism into Z, and the maximal height difference of the Gaussian random field, are presented.

In a variety of emerging applications one needs to decide whethera graph G matches another Gp, i.e., whether G has a topologicalstructure similar to that of Gp. The traditional notions of graphhomomorphism and isomorphism often fall short of capturing thestructural similarity in these applications. This paper studies revisions of these notions, providing a full treatment from co...