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33
On Linear Layouts of Graphs
, 2004
"... In a total order of the vertices of a graph, two edges with no endpoint in common can be crossing, nested, or disjoint. A kstack (resp... ..."
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Cited by 32 (20 self)
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In a total order of the vertices of a graph, two edges with no endpoint in common can be crossing, nested, or disjoint. A kstack (resp...
Discrete mathematics and radio channel assignment, in “Recent advances in theoretical and applied discrete mathematics
"... The radio channel assignment problem has recently sparked off much research in discrete applied mathematics, based on models that extend the idea of graph colouring. This is the subject of the present chapter. 1 ..."
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Cited by 19 (0 self)
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The radio channel assignment problem has recently sparked off much research in discrete applied mathematics, based on models that extend the idea of graph colouring. This is the subject of the present chapter. 1
Graphs and partially ordered sets: recent results and new directions
 JACOBSON (EDS.), SURVEYS IN GRAPH THEORY, CONGRESSUS NUMERANTIUM
, 1996
"... We survey some recent research progress on topics linking graphs and finite partially ordered sets. Among these topics are planar graphs, hamiltonian cycles and paths, graph and hypergraph coloring, online algorithms, intersection graphs, inclusion orders, random methods and ramsey theory. In each ..."
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Cited by 9 (2 self)
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We survey some recent research progress on topics linking graphs and finite partially ordered sets. Among these topics are planar graphs, hamiltonian cycles and paths, graph and hypergraph coloring, online algorithms, intersection graphs, inclusion orders, random methods and ramsey theory. In each case, we discuss open problems and future research directions.
New perspectives on interval orders and interval graphs
 in Surveys in Combinatorics
, 1997
"... Abstract. Interval orders and interval graphs are particularly natural examples of two widely studied classes of discrete structures: partially ordered sets and undirected graphs. So it is not surprising that researchers in such diverse fields as mathematics, computer science, engineering and the so ..."
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Cited by 9 (5 self)
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Abstract. Interval orders and interval graphs are particularly natural examples of two widely studied classes of discrete structures: partially ordered sets and undirected graphs. So it is not surprising that researchers in such diverse fields as mathematics, computer science, engineering and the social sciences have investigated structural, algorithmic, enumerative, combinatorial, extremal and even experimental problems associated with them. In this article, we survey recent work on interval orders and interval graphs, including research on online coloring, dimension estimates, fractional parameters, balancing pairs, hamiltonian paths, ramsey theory, extremal problems and tolerance orders. We provide an outline of the arguments for many of these results, especially those which seem to have a wide range of potential applications. Also, we provide short proofs of some of the more classical results on interval orders and interval graphs. Our goal is to provide fresh insights into the current status of research in this area while suggesting new perspectives and directions for the future. 1.
On the classes of minimal circularimperfect graphs
, 2008
"... Circularperfect graphs form a natural superclass of perfect graphs: on the one hand due to their definition by means of a more general coloring concept, on the other hand as an important class of χbound graphs with the smallest nontrivial χbinding function χ(G) ≤ ω(G) + 1. The Strong Perfect Gr ..."
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Cited by 7 (3 self)
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Circularperfect graphs form a natural superclass of perfect graphs: on the one hand due to their definition by means of a more general coloring concept, on the other hand as an important class of χbound graphs with the smallest nontrivial χbinding function χ(G) ≤ ω(G) + 1. The Strong Perfect Graph Conjecture, recently settled by Chudnovsky et al. [4], provides a characterization of perfect graphs by means of forbidden subgraphs. It is, therefore, natural to ask for an analogous conjecture for circularperfect graphs, that is for a characterization of all minimal circularimperfect graphs. At present, not many minimal circularimperfect graphs are known. This paper studies the circular(im)perfection of some families of graphs: normalized circular cliques, partitionable graphs, planar graphs, and complete joins. We thereby exhibit classes of minimal circularimperfect graphs, namely, certain partitionable webs, a subclass of planar graphs, and odd wheels and odd antiwheels. As those classes appear to be very different from a structural point of view, we infer that formulatingan appropriate conjecture for circularperfect graphs, as analogue to the Strong Perfect Graph Theorem, seems to be difficult.
Vertex Colouring and Forbidden Subgraphs  a Survey
, 2003
"... There is a great variety of colouring concepts and results in the literature. Here our focus is to survey results on vertex colourings of graphs de ned in terms of forbidden induced subgraph conditions. ..."
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Cited by 6 (0 self)
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There is a great variety of colouring concepts and results in the literature. Here our focus is to survey results on vertex colourings of graphs de ned in terms of forbidden induced subgraph conditions.
Coloring intersection graphs of geometric figures, in: Towards a Theory of Geometric Graphs
 Contemporary Mathematics 342, Amer. Math. Soc
, 2004
"... given clique number ..."
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