Parity vertex colorings of binomial trees

Petr Gregor, and Riste Škrekovski. "Parity vertex colorings of binomial trees." Discussiones Mathematicae Graph Theory 32.1 (2012): 177-180. <http://eudml.org/doc/271007>.

@article{PetrGregor2012,
abstract = {We show for every k ≥ 1 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 from [1] 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.},
author = {Petr Gregor, Riste Škrekovski},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {binomial tree; parity coloring; vertex ranking},
language = {eng},
number = {1},
pages = {177-180},
title = {Parity vertex colorings of binomial trees},
url = {http://eudml.org/doc/271007},
volume = {32},
year = {2012},
}

TY - JOUR
AU - Petr Gregor
AU - Riste Škrekovski
TI - Parity vertex colorings of binomial trees
JO - Discussiones Mathematicae Graph Theory
PY - 2012
VL - 32
IS - 1
SP - 177
EP - 180
AB - We show for every k ≥ 1 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 from [1] 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.
LA - eng
KW - binomial tree; parity coloring; vertex ranking
UR - http://eudml.org/doc/271007
ER -