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  • Ordered set  (2)
  • 05 C 70  (1)
  • computational complexity  (1)
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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Combinatorica 16 (1996), S. 407-412 
    ISSN: 1439-6912
    Keywords: 05 C 38 ; 05 C 70
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We show that if $$\sum\limits_{x \in S} {\deg _{G^x } \geqslant \left| G \right|}$$ , for every stable set $$S \subseteq V\left( G \right),\left| S \right| = k$$ , then the vertex set ofG can be covered withk−1 cycles, edges or vertices. This settles a conjecture by Enomoto, Kaneko and Tuza.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Order 11 (1994), S. 149-158 
    ISSN: 1572-9273
    Keywords: 06A07 ; Ordered set ; antichain ; fibre
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We show that in an ordered setP of width 3 there always exists a fibre (i.e., a subset intersecting each maximal nontrivial antichain) of size at most 11/18|P|. This improves previously known results.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Order 11 (1994), S. 343-351 
    ISSN: 1572-9273
    Keywords: 06A07 ; 68R10 ; Ordered set ; chain partition ; computational complexity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Lete be a fixed family of chains, i.e.e $$ \subseteq \{ \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{1} ,\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{2} ,\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{3} ,...\} $$ . Ae-partition of an ordered setP=(X, ⩽) is a partition ofX into subsets inducing chains isomorphic to the members ofe. In this paper we classify according to the computational complexity problems of existence of ae-partition ofP.
    Type of Medium: Electronic Resource
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