TY - JOUR
T1 - Trapezoid graphs and their coloring
AU - Dagan, Ido
AU - Golumbic, Martin Charles
AU - Pinter, Ron Yair
PY - 1988/9
Y1 - 1988/9
N2 - 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.
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.
UR - http://www.scopus.com/inward/record.url?scp=38049084478&partnerID=8YFLogxK
U2 - 10.1016/0166-218x(88)90032-7
DO - 10.1016/0166-218x(88)90032-7
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AN - SCOPUS:38049084478
SN - 0166-218X
VL - 21
SP - 35
EP - 46
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
IS - 1
ER -