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Discussiones Mathematicae Graph Theory 22(1) (2002) 89-99
DOI: https://doi.org/10.7151/dmgt.1159

PARTIAL COVERS OF GRAPHS

Jirí Fiala and  Jan Kratochvíl

Department of Applied Mathematics and Institute
for Theoretical Computer Science, Charles University
Malostranské nám. 25, 118 00 Prague, Czech Republic
e-mail: fiala@kam.mff.cuni.cz
e-mail: honza@kam.mff.cuni.cz

Abstract

Given graphs G and H, a mapping f:V(G)→ V(H) is a homomorphism if (f(u),f(v)) is an edge of H for every edge (u,v) of G. In this paper, we initiate the study of computational complexity of locally injective homomorphisms called partial covers of graphs. We motivate the study of partial covers by showing a correspondence to generalized (2,1)-colorings of graphs, the notion stemming from a practical problem of assigning frequencies to transmitters without interference. We compare the problems of deciding existence of partial covers and of full covers (locally bijective homomorphisms), which were previously studied.

Keywords: covering projection, computational complexity, graph homomorphism

2000 Mathematics Subject Classification: 05C85, 05C78.

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Received 7 August 2000
Revised 18 June 2001