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Graph Relabelling Systems and Distributed Algorithms
 HANDBOOK OF GRAPH GRAMMARS AND COMPUTING BY GRAPH TRANSFORMATION
, 1999
"... Graph relabelling systems have been introduced as a suitable model for expressing and studying distributed algorithms on a network of communicating processors. We recall the basic ideas underlying that model and we present the main questions that have been considered and the main results that have b ..."
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Cited by 28 (4 self)
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Graph relabelling systems have been introduced as a suitable model for expressing and studying distributed algorithms on a network of communicating processors. We recall the basic ideas underlying that model and we present the main questions that have been considered and the main results that have been obtained in that framework.
Locally Constrained Graph Homomorphisms  Structure, Complexity, and Applications
, 2013
"... A graph homomorphism is an edge preserving vertex mapping between two graphs. Locally constrained homomorphisms are those that behave well on the neighborhoods of vertices — if the neighborhood of any vertex of the source graph is mapped bijectively (injectively, surjectively) to the neighborhood of ..."
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Cited by 11 (1 self)
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A graph homomorphism is an edge preserving vertex mapping between two graphs. Locally constrained homomorphisms are those that behave well on the neighborhoods of vertices — if the neighborhood of any vertex of the source graph is mapped bijectively (injectively, surjectively) to the neighborhood of its image in the target graph, the homomorphism is called locally bijective (injective, surjective, respectively). We show that this view unifies issues studied before from different perspectives and under different names, such as graph covers, distance constrained graph labelings, or role assignments. Our survey provides an overview of applications, complexity results, related problems, and historical notes on locally constrained graph homomorphisms.
The Computational Complexity of the Role Assignment Problem
, 2002
"... A graph G is Rrole assignable if there is a locally surjective homomorphism from G to R, i.e. a vertex mapping r : VG ! VR , such that the neighborhood relation is preserved: r(NG(u)) = NR (r(u)). ..."
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Cited by 10 (2 self)
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A graph G is Rrole assignable if there is a locally surjective homomorphism from G to R, i.e. a vertex mapping r : VG ! VR , such that the neighborhood relation is preserved: r(NG(u)) = NR (r(u)).
Generalized Hcoloring and Hcovering of Trees
, 2002
"... We study H(p; q)colorings of graphs, for H a xed simple graph and p; q natural numbers, a generalization of various other vertex partitioning concepts such as Hcovering. An Hcover of a graph G is a local isomorphism between G and H, and the complexity of deciding if an input graph G has an H ..."
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Cited by 4 (1 self)
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We study H(p; q)colorings of graphs, for H a xed simple graph and p; q natural numbers, a generalization of various other vertex partitioning concepts such as Hcovering. An Hcover of a graph G is a local isomorphism between G and H, and the complexity of deciding if an input graph G has an Hcover is still open for many graphs H.
Complexity of Colored Graph Covers I. Colored Directed Multigraphs.
"... A covering projection from a graph G onto a graph H is a "local isomorphism": a mapping from the vertex set of G onto the vertex set of H such that, for every v 2 V (G), the neighborhood of v is mapped bijectively onto the neighborhood (in H) of the image of v. We continue the investig ..."
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Cited by 2 (1 self)
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A covering projection from a graph G onto a graph H is a "local isomorphism": a mapping from the vertex set of G onto the vertex set of H such that, for every v 2 V (G), the neighborhood of v is mapped bijectively onto the neighborhood (in H) of the image of v. We continue the investigation of the computational complexity of the Hcover problem  deciding if a given graph G covers H. We introduce a more general notion of covers of directed colored multigraphs (cdmgraphs) and show that a complete characterization of the complexity of covering of simple undirected graphs would necessarily resolve the complexity of covering of cdmgraphs as well. On the other hand, we introduce reductions that will enable to consider only multigraphs with minimum degree 3. We illustrate the methodology by presenting a complete characterization of the complexity of covering problems for twovertex cdmgraphs. 1 Motivation and Overview For a fixed graph H , the Hcover problem admits a gra...
Packing bipartite graphs with covers of complete bipartite graphs
 Proc 7th Int Conf on Algorithms and Complexity, Lecture Notes in Computer Science
, 2010
"... Abstract. For a set S of graphs, a perfect Spacking (Sfactor) of a graph G is a set of mutually vertexdisjoint subgraphs of G that each are isomorphic to a member of S and that together contain all vertices of G. IfG allows a covering (locally bijective homomorphism) to a graph H, thenG is an Hc ..."
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Abstract. For a set S of graphs, a perfect Spacking (Sfactor) of a graph G is a set of mutually vertexdisjoint subgraphs of G that each are isomorphic to a member of S and that together contain all vertices of G. IfG allows a covering (locally bijective homomorphism) to a graph H, thenG is an Hcover. For some fixed H let S(H) consist of all Hcovers. Let Kk,ℓ be the complete bipartite graph with partition classes of size k and ℓ, respectively. For all fixed k, ℓ ≥ 1, we determine the computational complexity of the problem that tests if a given bipartite graph has a perfect S(Kk,ℓ)packing. Our technique is partially based on exploring a close relationship to pseudocoverings. A pseudocovering from a graph G to a graph H is a homomorphism from G to H that becomes a covering to H when restricted to a spanning subgraph of G. We settle the computational complexity of the problem that asks if a graph allows a pseudocovering to Kk,ℓ for all fixed k, ℓ ≥ 1. 1