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  1. SIAM Journal on Discrete Mathematics (SJDMEC)
  2. Volume 17
  3. Volume 17 Issue 1
  4. Acyclic Homomorphisms and Circular Colorings of Digraphs
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Volume 32
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Volume 24
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Volume 18
Volume 17
Volume 17 Issue 4
Volume 17 Issue 3
Volume 17 Issue 2
Volume 17 Issue 1
Acyclic Homomorphisms and Circular Colorings of Digraphs
Comparing Top k Lists
Cooperative Games under Augmenting Systems
The Complexity of the Extendibility Problem for Finite Posets
On Z2k -Linear and Quaternary Codes
Constrained Edge-Splitting Problems
Detachments Preserving Local Edge-Connectivity of Graphs
On the Homology of the h,k-Equal Dowling Lattice
Internet Routing and Related Topology Issues
Some New Aspects of the Coupon Collector's Problem
Volume 16
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Volume 14
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Volume 12
Volume 11
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Volume 9
Volume 8
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Volume 2
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Acyclic Homomorphisms and Circular Colorings of Digraphs

Content Provider Society for Industrial and Applied Mathematics (SIAM)
Author Mohar, Bojan Feder, Toms Hell, Pavol
Copyright Year 2003
Abstract An acyclic homomorphism of a digraph D into a digraph F is a mapping $\phi\colon V(D) \to V(F)$ such that for every arc $uv\in E(D)$, either $\phi(u)=\phi(v)$ or $\phi(u)\phi(v)$ is an arc of F, and for every vertex $v\in V(F)$, the subgraph of D induced on $\phi^{-1}(v)$ is acyclic. For each fixed digraph F we consider the following decision problem: Does a given input digraph D admit an acyclic homomorphism to F? We prove that this problem is NP-complete unless F is acyclic, in which case it is polynomial time solvable. From this we conclude that it is NP-complete to decide if the circular chromatic number of a given digraph is at most q, for any rational number $q > 1$. We discuss the complexity of the problems restricted to planar graphs. We also refine the proof to deduce that certain F-coloring problems are NP-complete.
Starting Page 161
Ending Page 169
Page Count 9
File Format PDF
ISSN 08954801
DOI 10.1137/S0895480103422184
e-ISSN 10957146
Journal SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number 1
Volume Number 17
Language English
Publisher Society for Industrial and Applied Mathematics
Publisher Date 2006-08-01
Access Restriction Subscribed
Subject Keyword Computational difficulty of problems circular coloring graph homomorphism digraph circular chromatic number NP-completeness Directed graphs (digraphs), tournaments acyclic homomorphism Coloring of graphs and hypergraphs
Content Type Text
Resource Type Article
Subject Mathematics
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