Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4651313 | Discrete Mathematics | 2006 | 7 Pages |
Abstract
In this paper, we prove that the αα-labeling number of trees T , Tα⩽⌈r/2⌉nTα⩽⌈r/2⌉n where n=|E(T)|n=|E(T)| and r is the radius of T . This improves the known result Tα⩽eO(nlogn) tremendously and this upper bound is very close to the upper bound Tα⩽nTα⩽n conjectured by Snevily. Moreover, we prove that a tree with n edges and radius r decomposes KtKt for some t⩽(r+1)n2+1t⩽(r+1)n2+1.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Chin-Lin Shiue, Hung-Lin Fu,