ArticleOriginal scientific text
Title
Parity vertex colorings of binomial trees
Authors 1, 2
Affiliations
- Department of Theoretical Computer Science and Math. Logic, Charles University, Malostranské nám. 25, 118 00 Prague, Czech Republic
- Department of Mathematics, University of Ljubljana, Jadranska 21, 1000 Ljubljana, Slovenia
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.
Keywords
binomial tree, parity coloring, vertex ranking
Bibliography
- 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.
- 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.
- 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.
Pages:
177-180
Main language of publication
English
Received
2010-10-25
Accepted
2011-02-10
Published
2012
DOI: 10.7151/dmgt.1595
Exact and natural sciences