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Some Bounds for the Number of Blocks II

โœ Scribed by Ryuzaburou Noda


Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
95 KB
Volume
22
Category
Article
ISSN
0195-6698

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โœฆ Synopsis


The block sets achieving the bound ฮฒ(i) with i = 2 in Proposition 0 is studied. It is proved that such block sets exist if and only if some t-designs with prescribed parameters exist (Theorem 1).


๐Ÿ“œ SIMILAR VOLUMES


Some Bounds for the Number of Blocks
โœ Ryuzaburou Noda ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 65 KB

Some natural upper bounds for the number of blocks are given. Only a few block sets achieving the bounds except trivial ones are known. Necessary conditions for the existence of such block sets are given.

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Let f (v, e, ฮป) denote the maximum number of proper vertex colorings of a graph with v vertices and e edges in ฮป colors. In this paper we present some new upper bounds for f (v, e, ฮป). In particular, a new notion of pseudoproper colorings of a graph is given, which allows us to significantly improve

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## Abstract The upper bound for the harmonious chromatic number of a graph given by Zhikang Lu and by C. McDiarmid and Luo Xinhua, independently (__Journal of Graph Theory__, 1991, pp. 345โ€“347 and 629โ€“636) and the lower bound given by D. G. Beane, N. L. Biggs, and B. J. Wilson (__Journal of Graph T