TY - GEN
T1 - Anagram-free chromatic number is not pathwidth-bounded
AU - Carmi, Paz
AU - Dujmović, Vida
AU - Morin, Pat
N1 - Funding Information:
This work was partly funded by NSERC and the Ontario Ministry of Research, Innovation and Science. This work is based on work performed while attending the AlgoPARC Workshop on Parallel Algorithms and Data Structures at the University of Hawaii at Manoa, in part supported by the National Science Foundation under Grant No. 1745331.
Funding Information:
This work was partly funded by NSERC and the Ontario Ministry of Research, Innovation and Science. This work is based on work performed while attending the AlgoPARC Workshop on Parallel Algorithms and Data Structures at the University of Hawaii at Manoa, in part supported by the National Science Foundation under Grant No. 1745331. 1 A tree decomposition (T,B) of a graph G consists of a tree T and set B = {Bx : x ∈ V (T )} of subsets of V (G) called bags that are indexed by the nodes of T with the following properties:
Publisher Copyright:
© 2018, Springer Nature Switzerland AG.
PY - 2018/1/1
Y1 - 2018/1/1
N2 - The anagram-free chromatic number is a new graph parameter introduced independently by Kamčev, Łuczak, and Sudakov [1] and Wilson and Wood [5]. In this note, we show that there are planar graphs of pathwidth 3 with arbitrarily large anagram-free chromatic number. More specifically, we describe 2n-vertex planar graphs of pathwidth 3 with anagram-free chromatic number Ω(log n). We also describe kn vertex graphs with pathwidth 2 k- 1 having anagram-free chromatic number in Ω(klog n).
AB - The anagram-free chromatic number is a new graph parameter introduced independently by Kamčev, Łuczak, and Sudakov [1] and Wilson and Wood [5]. In this note, we show that there are planar graphs of pathwidth 3 with arbitrarily large anagram-free chromatic number. More specifically, we describe 2n-vertex planar graphs of pathwidth 3 with anagram-free chromatic number Ω(log n). We also describe kn vertex graphs with pathwidth 2 k- 1 having anagram-free chromatic number in Ω(klog n).
UR - http://www.scopus.com/inward/record.url?scp=85053460341&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-00256-5_8
DO - 10.1007/978-3-030-00256-5_8
M3 - Conference contribution
AN - SCOPUS:85053460341
SN - 9783030002558
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 91
EP - 99
BT - Graph-Theoretic Concepts in Computer Science - 44th International Workshop, WG 2018, Proceedings
A2 - Brandstädt, Andreas
A2 - Köhler, Ekkehard
A2 - Meer, Klaus
PB - Springer Verlag
T2 - 44th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2018
Y2 - 27 June 2018 through 29 June 2018
ER -