The Complexity of Chromatic Number When Restricted to graphs with Bounded Genus or Bounded Crossing Number-Reference-Cited by-同舟云学术

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The Complexity of Chromatic Number When Restricted to graphs with Bounded Genus or Bounded Crossing Number

Published:2022-06-10 Issue:2 Volume:53 Page:27-38
ISSN:0163-5700
Container-title:ACM SIGACT News
language:en
Short-container-title:SIGACT News

Author:

Gasarch William¹,Hayes Nathan¹,Ostuni Anthony²,Park Davin¹

Affiliation:

1. University of Maryland at College Park

2. University of California, San Diego

Abstract

e present a known theorem with the following authors. Part 1 was proven by Hopcroft and Tarjan [10]. Part 2 is easy. Part 3 was proven by Garey, Johnson, and Stockmeyer [6]. Part 4 was proven by Appel, Haken, and Koch [2, 3].

Publisher

Association for Computing Machinery (ACM)

Subject

General Materials Science

Link

https://dl.acm.org/doi/pdf/10.1145/3544979.3544987

Reference23 articles.

1. M. O. Albertson , D. W. Cranston , and J. Fox . Crossings, colorings, and cliques. Elec- tronic Journal of Combinatorics, 16(1) , 2009 . http://math.mit.edu/~fox/paper-crossingcoloring.pdf. M. O. Albertson, D. W. Cranston, and J. Fox. Crossings, colorings, and cliques. Elec- tronic Journal of Combinatorics, 16(1), 2009. http://math.mit.edu/~fox/paper-crossingcoloring.pdf.

2. Every planar map is four colorable. Part I: Discharging

3. Every planar map is four colorable. Part II: Reducibility

4. J. Bar--at and G. T--oth . Towards the Albertson conjecture. Electronic Journal Combina- torics, 17(1) , 2010 . https://arxiv.org/abs/0909.0413. J. Bar--at and G. T--oth. Towards the Albertson conjecture. Electronic Journal Combina- torics, 17(1), 2010. https://arxiv.org/abs/0909.0413.

5. 5-Coloring Graphs with 4 Crossings

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