Complexity results for minimum sum edge coloring

被引：9
|
作者：
Daniel Marx [1 ]
机构：
[1] Budapest Univ Technol & Econ, Dept Comp Sci & Informat Theory, H-1521 Budapest, Hungary
来源：
DISCRETE APPLIED MATHEMATICS | 2009年 / 157卷 / 05期
关键词：
Graph coloring; Minimum sum coloring; NP-completeness; PRECOLORING EXTENSION; CHROMATIC SUM; INTERVAL; COMPLETENESS; ALGORITHM; GRAPHS;
D O I：
10.1016/j.dam.2008.04.002
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the MINIMUM SUM EDGE COLORING problem we have to assign positive integers to the edges of a graph such that adjacent edges receive different integers and the sum of the assigned numbers is minimal. We show that the problem is (a) NP-hard for planar bipartite graphs with maximum degree 3. (b) NP-hard for 3-regular planar graphs, (c) NP-hard for partial 2-trees, and (d) APX-hard for bipartite graphs. (C) 2008 Elsevier B.V. All rights reserved.
引用
收藏
页码：1034 / 1045
页数：12
相关论文
共 50 条
  • [31] A branch-and-price algorithm for the Minimum Sum Coloring Problem
    Delle Donne, Diego
    Furini, Fabio
    Malaguti, Enrico
    Calvo, Roberto Wolfler
    [J]. DISCRETE APPLIED MATHEMATICS, 2021, 303 : 39 - 56
  • [32] On the Minimum Sum Coloring of P4-Sparse Graphs
    Flavia Bonomo
    Mario Valencia-Pabon
    [J]. Graphs and Combinatorics, 2014, 30 : 303 - 314
  • [33] Minimum sum set coloring of trees and line graphs of trees
    Bonomo, Flavia
    Duran, Guillermo
    Marenco, Javier
    Valencia-Pabon, Mario
    [J]. DISCRETE APPLIED MATHEMATICS, 2011, 159 (05) : 288 - 294
  • [34] A branch-and-price algorithm for the Minimum Sum Coloring Problem
    Delle Donne, Diego
    Furini, Fabio
    Malaguti, Enrico
    Wolfler Calvo, Roberto
    [J]. Discrete Applied Mathematics, 2021, 303 : 39 - 56
  • [35] Behavior study of genetic operators for the minimum sum coloring problem
    Bouziri, Hend
    Harrabi, Olfa
    [J]. 2013 5TH INTERNATIONAL CONFERENCE ON MODELING, SIMULATION AND APPLIED OPTIMIZATION (ICMSAO), 2013,
  • [36] On the Parallel Complexity of Minimum Sum of Diameters Clustering
    Juneam, Nopadon
    Kantabutra, Sanpawat
    [J]. 2015 INTERNATIONAL COMPUTER SCIENCE AND ENGINEERING CONFERENCE (ICSEC), 2015, : 124 - 129
  • [37] Complexity and algorithms for injective edge-coloring in graphs
    Foucaud, Florent
    Hocquard, Herve
    Lajou, Dimitri
    [J]. INFORMATION PROCESSING LETTERS, 2021, 170
  • [38] The Complexity of (List) Edge-Coloring Reconfiguration Problem
    Osawa, Hiroki
    Suzuki, Akira
    Ito, Takehiro
    Zhou, Xiao
    [J]. WALCOM: ALGORITHMS AND COMPUTATION, WALCOM 2017, 2017, 10167 : 347 - 358
  • [39] Complexity of approximation of 3-edge-coloring of graphs
    Kochol, Martin
    Krivonakova, Nad'a
    Smejova, Silvia
    Srankova, Katarina
    [J]. INFORMATION PROCESSING LETTERS, 2008, 108 (04) : 238 - 241
  • [40] The Complexity of 2-Coloring and Strong Coloring in Uniform Hypergraphs of High Minimum Degree
    Szymanska, Edyta
    [J]. DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE, 2013, 15 (02): : 121 - 138
12345