Trapezoid graphs and their coloring

Ido Dagan; Martin Charles Golumbic; Ron Yair Pinter

doi:10.1016/0166-218X(88)90032-7

Trapezoid graphs and their coloring

Ido Dagan, Martin Charles Golumbic, Ron Yair Pinter

Research output: Contribution to journal › Article › peer-review

Abstract

We define trapezoid graphs, an extension of both interval and permutation graphs. We show that this new class properly contains the union of the two former classes, and that trapezoid graphs are equivalent to the incomparability graphs of partially ordered sets having interval order dimension at most two. We provide an optimal coloring algorithm for trapezoid graphs that runs in time O(nk), where n is the number of nodes and k is the chromatic number of the graph. Our coloring algorithm has direct applications to channel routing on integrated circuits.

Original language	English
Pages (from-to)	35-46
Number of pages	12
Journal	Discrete Applied Mathematics
Volume	21
Issue number	1
DOIs	https://doi.org/10.1016/0166-218X(88)90032-7
State	Published - Sep 1988
Externally published	Yes

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/0166-218X(88)90032-7

Cite this

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abstract = "We define trapezoid graphs, an extension of both interval and permutation graphs. We show that this new class properly contains the union of the two former classes, and that trapezoid graphs are equivalent to the incomparability graphs of partially ordered sets having interval order dimension at most two. We provide an optimal coloring algorithm for trapezoid graphs that runs in time O(nk), where n is the number of nodes and k is the chromatic number of the graph. Our coloring algorithm has direct applications to channel routing on integrated circuits.",

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AB - We define trapezoid graphs, an extension of both interval and permutation graphs. We show that this new class properly contains the union of the two former classes, and that trapezoid graphs are equivalent to the incomparability graphs of partially ordered sets having interval order dimension at most two. We provide an optimal coloring algorithm for trapezoid graphs that runs in time O(nk), where n is the number of nodes and k is the chromatic number of the graph. Our coloring algorithm has direct applications to channel routing on integrated circuits.

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Trapezoid graphs and their coloring

Abstract

ASJC Scopus subject areas

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