For a set S of graphs, a perfect S-packing (S-factor) of a graph G is a set of mutually vertex-disjoint subgraphs of G that each are isomorphic to a member of S and that together contain all vertices of G. If G allows a covering (locally bijective homomorphism) to a graph H, i.e., a vertex mapping f : VG → VH satisfying the property that f(u)f(v) belongs to EH whenever the edge uv belongs to EG...

In this note we recall some well-known results about covering and k-covering of graphs. Then, we introduce a new notion of spanning tree which we call the p-spanning tree. This notion allows us to reduce the upper bound for the minimum integer k for which a connected graph G has no nontrivial k-covering. This note deals with the notion of covering of graphs and more precisely with the notion of...

We present a necessary and sufficient condition for a graph of odd-girth 2k + 1 to bound the class of K4-minor-free graphs of odd-girth (at least) 2k + 1, that is, to admit a homomorphism from any such K4-minor-free graph. This yields a polynomial-time algorithm to recognize such bounds. Using this condition, we first prove that every K4-minor free graph of odd-girth 2k+1 admits a homomorphism ...

A graph matching algorithm is illustrated and its performance compared with that of a well known algorithm performing the same task. According to the proposed algorithm, the matching process is carried out by using a State Space Representation: a state represents a partial solution of the matching between two graphs, and a transition between states corresponds to the addition of a new pair of m...

We introduce a novel technique to give bounds to the entangled value of non-local games. The technique is based on a class of graphs used by Cabello, Severini and Winter in 2010. The upper bound uses the famous Lovász theta number and is efficiently computable; the lower one is based on the quantum independence number, which is a quantity used in the study of entanglementassisted channel capaci...

We consider a model of a random height function with long-range constraints on a discrete segment. This model was suggested by Benjamini, Yadin and Yehudayoff and is a generalization of simple random walk. The random function is uniformly sampled from all graph homomorphisms from the graph Pn,d to the integers Z, where the graph Pn,d is the discrete segment {0, 1, . . . , n} with edges between ...

Scene interpretation guided by a generic model benefits from structural representations of objects and their spatial relationships. In this paper, we consider nested conceptual graphs for encoding objects and groups of objects, spatial relationships between objects or between groups of objects, along with the imprecision and uncertainty attached to the formal representations of such relationshi...

Covering arrays are combinatorial designs that are used for testing systems such as software, circuits and networks, where failures can be caused by the interaction between their components or parameters. New generalizations of these objects employ techniques from design theory, graph homomorphisms, combinatorial group testing, among other fields. This minisymposium highlights current research ...

This paper answers the SCG-1 initiative. The room allocation problem provided has been solved in a generic and automatic way. The solution is based on a totally declarative formal model. Basic constructs are simple graphs and the fundamental operation for doing reasonings is the graph morphism known as projection. The other formal constructs are rules and constraints defined in terms of simple ...

Working with system-designing one has often to transform a simple, but usually not readable model of a system to a more complicated but easier to analyzing form. In the paper Petri nets of a class are represented as members of an equationally deened class of structures. This representation leads to a relatively simple description of some typical constructions on Petri nets e.g. products and cop...