Note on 3-Coloring of (2P4, C5)-Free Graphs

We show that the 3-coloring problem is polynomial-time solvable on $(2P_4,C_5)$-free graphs.

[1]  Petr A. Golovach,et al.  List Coloring in the Absence of a Linear Forest , 2011, Algorithmica.

[2]  Quasi-polynomial-time algorithm for Independent Set in Pt-free and C>t-free graphs via shrinking the space of connecting subgraphs , 2020, ArXiv.

[3]  M. Krom.  The Decision Problem for a Class of First‐Order Formulas in Which all Disjunctions are Binary , 1967 .

[4]  Jian Song,et al.  Coloring graphs without short cycles and long induced paths , 2014, Discret. Appl. Math..

[5]  Colouring (Pr + Ps)-Free Graphs , 2020, Algorithmica.

[6]  Flavia Bonomo-Braberman,et al.  Better 3-coloring algorithms: Excluding a triangle and a seven vertex path , 2021, Theor. Comput. Sci..

[7]  Maria Chudnovsky,et al.  Three-coloring graphs with no induced seven-vertex path I : the triangle-free case , 2014, ArXiv.

[9]  P. Seymour,et al.  The Strong Perfect Graph Theorem , 2002, math/0212070.

[10]  Shenwei Huang,et al.  Complexity of coloring graphs without paths and cycles , 2017, Discret. Appl. Math..

[11]  Jian Song,et al.  Closing complexity gaps for coloring problems on H-free graphs , 2014, Inf. Comput..

[12]  Stefan Hougardy,et al.  Uniquely Colourable Graphs and the Hardness of Colouring Graphs of Large Girth , 1998, Combinatorics, Probability and Computing.

[13]  Jian Song,et al.  A Survey on the Computational Complexity of Coloring Graphs with Forbidden Subgraphs , 2014, J. Graph Theory.

[14]  Stanley M. Selkow,et al.  Some perfect coloring properties of graphs , 1979, J. Comb. Theory, Ser. B.

[15]  Michal Pilipczuk,et al.  Quasi-polynomial-time algorithm for Independent Set in Pt-free graphs via shrinking the space of induced paths , 2020, SOSA.

[16]  Zvi Galil,et al.  NP Completeness of Finding the Chromatic Index of Regular Graphs , 1983, J. Algorithms.

[17]  Maya Jakobine Stein,et al.  3-Colouring Pt-free graphs without short odd cycles , 2020, ArXiv.

[19]  Yehoshua Perl,et al.  Clustering and domination in perfect graphs , 1984, Discret. Appl. Math..

[20]  Maria Chudnovsky,et al.  Four-coloring P6-free graphs , 2019, SODA.

[21]  Maria Chudnovsky,et al.  Three-coloring graphs with no induced seven-vertex path II : using a triangle , 2015, ArXiv.

[22]  Ian Holyer,et al.  The NP-Completeness of Edge-Coloring , 1981, SIAM J. Comput..

[23]  L. Lovász,et al.  Polynomial Algorithms for Perfect Graphs , 1984 .

[24]  Maria Chudnovsky,et al.  List 3-coloring Pt-free graphs with no induced 1-subdivision of K1, s , 2020, Discret. Math..

[25]  Daniël Paulusma,et al.  Narrowing the Complexity Gap for Colouring (Cs, Pt)-Free Graphs , 2015, Comput. J..

[26]  Daniel Lokshtanov,et al.  Independent Set on $\mathrm{P}_{k}$-Free Graphs in Quasi-Polynomial Time , 2020, 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS).

[27]  Daniël Paulusma,et al.  Colouring (Pr + Ps)-Free Graphs , 2018, Algorithmica.

[28]  Maya Jakobine Stein,et al.  3-Colouring graphs without triangles or induced paths on seven vertices , 2014, ArXiv.

[29]  Maya Jakobine Stein,et al.  Three-Coloring and List Three-Coloring of Graphs Without Induced Paths on Seven Vertices , 2018, Comb..

[30]  Vadim V. Lozin,et al.  Deciding k-Colorability of P5-Free Graphs in Polynomial Time , 2007, Algorithmica.

[31]  Maria Chudnovsky,et al.  List-three-coloring Pt-free graphs with no induced 1-subdivision of K1, s , 2020, ArXiv.

[32]  Shenwei Huang,et al.  Improved complexity results on k-coloring Pt-free graphs , 2013, Eur. J. Comb..

[33]  Maria Chudnovsky,et al.  4‐Coloring P6‐Free Graphs with No Induced 5‐Cycles , 2014, J. Graph Theory.

[34]  Oliver Schaudt,et al.  Exhaustive generation of k‐critical H ‐free graphs , 2015, J. Graph Theory.

[35]  Maria Chudnovsky,et al.  3-Colorable Subclasses of P8-Free Graphs , 2018, SIAM J. Discret. Math..

[36]  Jian Song,et al.  Coloring graphs without short cycles and long induced paths , 2011, Discret. Appl. Math..