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On the complexity of H-coloring
TLDR
The natural conjecture, formulated in several sources, asserts that the H-coloring problem is NP-complete for any non-bipartite graph H, and a proof of this conjecture is given. Expand
Graphs and homomorphisms
  • P. Hell, J. Nesetril
  • Computer Science, Mathematics
  • Oxford lecture series in mathematics and its…
  • 2004
TLDR
This chapter discusses the structure of Composition, the partial order of Graphs and Homomorphisms, and testing for the Existence of Homomorphism. Expand
On the History of the Minimum Spanning Tree Problem
TLDR
There are several apparently independent sources and algorithmic solutions of the minimum spanning tree problem and their motivations, and they have appeared in Czechoslovakia, France, and Poland, going back to the beginning of this century. Expand
List Homomorphisms to Reflexive Graphs
  • T. Feder, P. Hell
  • Mathematics, Computer Science
  • J. Comb. Theory, Ser. B
  • 1 March 1998
TLDR
A polynomial time algorithm is given to solve the problem when the input graph is an interval graph and it is argued that the complexity of certain other modifications of the problem are likely to be difficult to classify. Expand
Linear-Time Representation Algorithms for Proper Circular-Arc Graphs and Proper Interval Graphs
TLDR
A linear-time algorithm to recognize and represent proper circular-arc graphs and obtain a new proof of a characterization of proper interval graphs by forbidden subgraphs. Expand
List Homomorphisms and Circular Arc Graphs
TLDR
It is shown that the list homomorphism problem is polynomial time solvable if the complement of H is a circular arc graph of clique covering number two, and is NP-complete otherwise. Expand
The core of a graph
TLDR
It is found that the core of a finite graph is unique (up to isomorphism) and is also its smallest retract, and some homomorphism properties of cores are investigated, concluding that it is NP-complete to decide whether a graph is its own core. Expand
A note on the star chromatic number
A. Vince introduced a natural generalization of graph coloring and proved some basic facts, revealing it to be a concept of interest. His work relies on continuous methods. In this note we make someExpand
Interval bigraphs and circular arc graphs
We prove that the complements of interval bigraphs are precisely those circular arc graphs of clique covering number two, which admit a representation without two arcs covering the whole circle. WeExpand
Graph Problems Arising from Wavelength-Routing in All-Optical Networks
We survey the theoretical results obtained for wavelength routing in al l-optical networks, present some new results and propose several open problems. In all-optical networks the vast band- widthExpand
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