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  • We show for every k that the binomial tree of order 3k has a vertex-coloring with 2k+1 colors such that every path contains some color odd number of times. This disproves a conjecture of Boroviecki, Budajová, Jenrol and Krajči asserting that for every tree T the minimal number of colors in a such coloring of T is at least the vertex ranking number of T minus one.
  • We show for every k that the binomial tree of order 3k has a vertex-coloring with 2k+1 colors such that every path contains some color odd number of times. This disproves a conjecture of Boroviecki, Budajová, Jenrol and Krajči asserting that for every tree T the minimal number of colors in a such coloring of T is at least the vertex ranking number of T minus one. (en)
Title
  • Parity vertex colorings of binomial trees
  • Parity vertex colorings of binomial trees (en)
skos:prefLabel
  • Parity vertex colorings of binomial trees
  • Parity vertex colorings of binomial trees (en)
skos:notation
  • RIV/00216208:11320/12:10103314!RIV13-GA0-11320___
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  • I, P(GP201/08/P298), P(MEB091037)
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  • 1
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  • 157846
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  • RIV/00216208:11320/12:10103314
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  • vertex ranking; parity coloring; binomial tree (en)
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  • PL - Polská republika
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  • [D63F906984E5]
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  • Discussiones Mathematicae - Graph Theory
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  • 32
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  • Gregor, Petr
  • Škrekovski, Riste
issn
  • 1234-3099
number of pages
http://bibframe.org/vocab/doi
  • 10.7151/dmgt.1595
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  • 11320
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