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A Sufficient Condition for Realizability of Constrained Graphs

J. M. Yohe
SIAM Journal on Applied Mathematics
Vol. 36, No. 1 (Feb., 1979), pp. 15-25
Stable URL: http://www.jstor.org/stable/2100764
Page Count: 11
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A Sufficient Condition for Realizability of Constrained Graphs
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Abstract

A constrained graph is a (simple, undirected) graph G together with a specified cyclic ordering of its vertices ν0, ⋯, νr - 1. We say that a constrained graph G is realizable provided that there exists a collection of polygonal arcs c0, ⋯, cr - 1 in the unit disk D2 in the plane such that ci ∩ BdD2 = {ai}, the cyclic ordering of the ai's around the boundary of D2 is the same as the cyclic ordering of the vertices of G, and ci ∩ cj ≠ φ if and only if viv j is an edge of G. In this paper we present a new sufficient condition for realizability of constrained graphs. The question of realizability of constrained graphs arises in the study of the feasibility of laying out thin-film RC circuits. The present paper extends work done by F. W. Sinden of Bell Laboratories.

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