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Planar graphs without 5- and 7-cycles and without adjacent triangles are 3-colorable

  • Published:2009-07 Issue:4 Volume:99 Page:668-673
  • ISSN:0095-8956
  • Container-title:Journal of Combinatorial Theory, Series B
  • language:en
  • Short-container-title:Journal of Combinatorial Theory, Series B

Author:

Borodin O.V.,Glebov A.N.,Montassier M.,Raspaud A.

Publisher

Elsevier BV

Subject

Computational Theory and Mathematics,Discrete Mathematics and Combinatorics,Theoretical Computer Science

Reference11 articles.

1. On small faces in 4-critical graphs;Abbott;Ars Combin.,1991

2. On extending 3-colorability from a 6-face to a planar triangle-free graph;Aksenov;Diskretn. Anal. Issled. Oper.,2003

3. Extending 3-colorability from a 7-face to a planar triangle-free graph;Aksenov;Sib. Elektron. Mat. Izv.,2004

4. To the paper of H.L. Abbott and B. Zhou on 4-critical planar graphs;Borodin;Ars Combin.,1996

5. Structural properties of plane graphs without adjacent triangles and an application to 3-colorings;Borodin;J. Graph Theory,1996

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1. Planar graphs having no cycle of length 4, 7, or 9 are DP‐3‐colorable;Journal of Graph Theory;2024-05-22

2. A Victorian Comedy of Errors and Colorful Progress;The New Mathematical Coloring Book;2024

3. $(I,F)$-partition of planar graphs without cycles of length 4, 6, or 9;Discussiones Mathematicae Graph Theory;2023

4. A note on the Three Color Problem on planar graphs without 4- and 5-cycles and without ext-triangular 7-cycles;Discrete Mathematics;2023-01

5. A counter example to Steinberg conjecture;INTERNATIONAL CONFERENCE ON RECENT ADVANCES IN MATHEMATICS AND COMPUTATIONAL ENGINEERING: ICRAMCE 2022;2023
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