A convex labeling of a tree T o f order n is a one-to-one function f from the vertex set of Tinto the nonnegative integers, so that f ( y ) 5 ( f ( x ) t f(z))/2 for every path x, y, z of length 2 in T. If, in addition, f (v) I n -1 for every vertex v of T, then f is a perfect convex labeling and T
✦ LIBER ✦
Distance three labelings of trees
✍ Scribed by Jiří Fiala; Petr A. Golovach; Jan Kratochvíl; Bernard Lidický; Daniël Paulusma
- Book ID
- 113564614
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 496 KB
- Volume
- 160
- Category
- Article
- ISSN
- 0166-218X
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## Abstract Let __T__ = (__V, E__) be a tree whose vertices are properly 2‐colored. A bipartite labeling of __T__ is a bijection __f__: __V__ ← {0, 1, ⃛, | __E__ |} for which there is a __k__ such that whenever __f__(__u__) ≤ __k__ < __f__(__v__), then __u__ and __v__ have different colors. The α‐s
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