# Parity vertex colorings of binomial trees

Discussiones Mathematicae Graph Theory (2012)

- Volume: 32, Issue: 1, page 177-180
- ISSN: 2083-5892

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topPetr 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 -

## References

top- [1] P. Borowiecki, K. Budajová, S. Jendrol' and S. Krajči, Parity vertex colouring of graphs, Discuss. Math. Graph Theory 31 (2011) 183-195, doi: 10.7151/dmgt.1537. Zbl1284.05091
- [2] D.P. Bunde, K. Milans, D.B. West and H. Wu, Parity and strong parity edge-colorings of graphs, Combinatorica 28 (2008) 625-632, doi: 10.1007/s00493-008-2364-3. Zbl1199.05105
- [3] A.A. Dobrynin, R. Entringer and I. Gutman, Wiener index of trees: theory and applications, Acta Appl. Math. 66 (2001) 211-249, doi: 10.1023/A:1010767517079. Zbl0982.05044

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