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  • Loebl, Komlós, and Sós conjectured that if at least half the vertices of a graph G have degree at least some k, then every tree with at most k edges is a subgraph of G. We prove the conjecture for all trees of diameter at most 5 and for a class of caterpillars. Our result implies a bound on the Ramsey number r(T,T') of trees T,T' from the above classes.
  • Loebl, Komlós, and Sós conjectured that if at least half the vertices of a graph G have degree at least some k, then every tree with at most k edges is a subgraph of G. We prove the conjecture for all trees of diameter at most 5 and for a class of caterpillars. Our result implies a bound on the Ramsey number r(T,T') of trees T,T' from the above classes. (en)
  • Domněnka Loebla, Komlóse a Sósové říká, že pokud alespoň polovina vrcholů grafu G má stupeň alespoň k, pak libovolný strom s k hranami je podgrafem grafu G. Dokážeme domněnku pro stromy o průměru 5 a pro určité třídy housenek. Náš výsledek implikuje horní mez pro Ramseyovo číslo r(T,T') pro stromy T a T' z výše uvedené třídy. (cs)
Title
  • The Loebl-Komlós-Sós conjecture for trees of diameter 5 and for certain caterpillars (Article No. R106)
  • Domněnka Loebla, Komlóse a Sósové pro stromy o průměru 5 a pro některé housenky (cs)
  • The Loebl-Komlós-Sós conjecture for trees of diameter 5 and for certain caterpillars (Article No. R106) (en)
skos:prefLabel
  • The Loebl-Komlós-Sós conjecture for trees of diameter 5 and for certain caterpillars (Article No. R106)
  • Domněnka Loebla, Komlóse a Sósové pro stromy o průměru 5 a pro některé housenky (cs)
  • The Loebl-Komlós-Sós conjecture for trees of diameter 5 and for certain caterpillars (Article No. R106) (en)
skos:notation
  • RIV/00216208:11320/08:00100025!RIV09-MSM-11320___
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  • 377042
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  • RIV/00216208:11320/08:00100025
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  • Loebl-Komlós-Sós; conjecture; trees; diameter; certain; caterpillars; Article (en)
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  • US - Spojené státy americké
http://linked.open...ontrolniKodProRIV
  • [7B9381D83762]
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  • Electronic Journal of Combinatorics
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  • 15
http://linked.open...iv/tvurceVysledku
  • Piguetová, Diana
  • Stein, Maya Jakobine
http://linked.open...ain/vavai/riv/wos
  • 000258476300001
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  • 1077-8926
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  • 11320
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