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Ordered sets with small width and large jump number

โœ Scribed by Weixuan Li; James H. Schmerl

Publisher
Springer Netherlands
Year
1986
Tongue
English
Weight
89 KB
Volume
3
Category
Article
ISSN
0167-8094

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โœฆ Synopsis

The following result is proved in this note: For any positive integers w and t, if an ordered set P has jump number at least (t + 1) w -', then either the width of P is moYe than w, or P has a tower, i.e., a linear sum of pairs of noncomparable elements, of height more than t. AhfS (MOS) subject classification (1980). 06AlO.

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Motivated by earlier work on dominating cliques, we show that if a graph G is connected and contains no induced subgraph isomorphic to P 6 or H t (the graph obtained by subdividing each edge of K 1,t , t โ‰ฅ 3, by exactly one vertex), then G has a dominating set which induces a connected graph with cl