Partial covers of graphs

Fiala, Jiřı́; Kratochvı́l, Jan

doi:10.7151/dmgt.1159

Cited by 52 publications

(42 citation statements)

References 14 publications

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“…Locally bijective homomorphisms are also called coverings and have applications in topological graph theory [26] and distributed computing [1,2]. The corresponding decision problems, called Partial Cover and Cover respectively, are NP-complete for arbitrary G even when R is fixed to be the complete graph on four vertices [11,19].…”

Section: Complementary Results and An Open Questionmentioning

confidence: 99%

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Computing Role Assignments of Proper Interval Graphs in Polynomial Time

Heggernes

Hof

Paulusma

2011

Lecture Notes in Computer Science

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Further information on publisher's website:http://dx.doi.org/10. 1016/j.jda.2011.12.004 Publisher's copyright statement: NOTICE: this is the author's version of a work that was accepted for publication in Journal of discrete algorithms. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be re ected in this document. Changes may have been made to this work since it was submitted for publication. A de nitive version was subsequently published in Journal of discrete algorithms, 14, 2012, 10.1016/j.jda.2011.12.004 Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractAn R-role assignment of a graph G is a locally surjective homomorphism from G to graph R. For a fixed graph R, the R-Role Assignment problem is to decide, for an input graph G, whether G has an R-role assignment. When both graphs G and R are given as input, the problem is called Role Assignment. In this paper, we study the latter problem. It is known that R-Role Assignment is NP-complete already when R is a path on three vertices. In order to obtain polynomial time algorithms for Role Assignment, it is therefore necessary to put restrictions on G. So far, the only known non-trivial case for which this problem is solvable in polynomial time is when G is a tree. We present an algorithm that solves Role Assignment in polynomial time when G is a proper interval graph. Thus we identify the first graph class other than trees on which the problem is tractable. As a complementary result, we show that Role Assignment is Graph Isomorphism-hard on chordal graphs, a superclass of proper interval graphs and trees.

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Section: Complementary Results and An Open Questionmentioning

confidence: 99%

“…Locally injective homomorphisms, also called partial coverings, have applications in frequency assignment [10] and telecommunication [11]. Locally bijective homomorphisms are also called coverings and have applications in topological graph theory [26] and distributed computing [1,2].…”

Section: Complementary Results and An Open Questionmentioning

confidence: 99%

Computing Role Assignments of Proper Interval Graphs in Polynomial Time

Heggernes

Hof

Paulusma

2011

Lecture Notes in Computer Science

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“…Some partial results can be found in [4,5,6,17,2]. It might be of independent interest that locally injective homomorphisms generalize the notion of L(2, 1)-labelings, which are motivated by the frequency assignment problem.…”

Section: Introductionmentioning

confidence: 99%

Dichotomy of the H-Quasi-Cover Problem

Fiala

Tesař

2013

Computer Science – Theory and Applications

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“…We say that f is locally injective [15] if |N G (u)| = |N H (f (u))| holds for all u ∈ V G . Using CHIPS conditions we can equivalently say that a homomorphism f from G to H is locally injective, locally bijective, or locally surjective if…”

Section: Example 1 Locally Constrained Homomorphismsmentioning

confidence: 99%

Graph Labelings Derived from Models in Distributed Computing

Chalopin

Paulusma

2006

Graph-Theoretic Concepts in Computer Science

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We discuss 11 known basic models of distributed computing: four message-passing models that differ by the (non)existence of port-numbers and a hierarchy of seven local computations models. In each of these models, we study the computational complexity of the decision problems if the leader election and if the naming problem can be solved on a given network. It is already known that these two decision problems are solvable in polynomial time for two models and are co-NP-complete for another one. Here, we settle the computational complexity for both problems in the remaining eight models by showing that they are co-NP-complete. We do this by translating each problem into a graph labeling problem. By using this technique, we also obtain an alternative proof for the already known co-NP-completeness result. In the second part of our article, we completely classify the computational complexity of all the corresponding graph labeling problems, i.e., for every fixed integer k ≥ 1 we determine the complexity of the problem that asks whether a given graph allows a certain graph labeling that uses at most k labels. We also explain the close relationship of these labelings to graph homomorphisms that satisfy some further (global or local) constraints. This yields a new class of "constrained" graph homomorphisms that include the already known locally constrained graph homomorphisms.

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Partial covers of graphs

Cited by 52 publications

References 14 publications

Computing Role Assignments of Proper Interval Graphs in Polynomial Time

Computing Role Assignments of Proper Interval Graphs in Polynomial Time

Dichotomy of the H-Quasi-Cover Problem

Graph Labelings Derived from Models in Distributed Computing

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