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A short proof of the degree bound for interval number

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Abstract

A short proof is given of the fact that every graph has an interval representation of depth 2 in which each vertex v is represented by at most 12(d(v)+1)⌋ intervals, except for an arbitrarily specified vertex w that appears left-most in the representation and is represented by at most 12;(d(w)+1)⌉ intervals.

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Research supported in part by ONR Grant N00014-85K0570 and by NSF grant DMS 8504322.