Title:
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Decomposing almost complete graphs by random trees
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Author:
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Lladó Sánchez, Ana M.
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV; Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions |
Abstract:
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An old conjecture of Ringel states that every tree with m edges decom- poses the complete graph K 2 m +1 . A more general version of the Ringel’s conjecture says that every tree with m edges decomposes K rm +1 for each r = 2 provided that r and m + 1 are not both odd. The best lower bound for the order of a complete graph decomposed by a given tree with m edge is O ( m 3 ). We show that asymptotically almost surely a random tree with m edges and p = 2 m + 1 is a prime decomposes the complete graph minus one edge K 3 p - e . We also show that, for every prime of the form 2 km + 1 a random tree with m edges asymptotically almost surely decomposes the graph K 2 km +1 (3) obtained from the complete graph by replacing each vertex by the complement of a triangle. |
Abstract:
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Peer Reviewed |
Subject(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs -Graph theory -Ringel Conjecture -random trees -Grafs, Teoria de -05C Graph theory |
Rights:
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Document type:
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Article - Published version Conference Object |
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