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Semi-balanced colorings of graphs: Generalized 2-colorings based on a relaxed discrepancy condition

Jansson, Jesper LU and Tokuyama, T (2004) In Graphs and Combinatorics 20(2). p.205-222
Abstract
We generalize the concept of a 2-coloring of a graph to what we call a semi-balanced coloring by relaxing a certain discrepancy condition on the shortest-paths hypergraph of the graph. Let G be an undirected, unweighted, connected graph with n vertices and m edges. We prove that the number of different semi-balanced colorings of G is: (1) at most n+1 if G is bipartite; (2) at most m if G is non-bipartite and triangle-free; and (3) at most m+1 if G is non-bipartite. Based on the above combinatorial investigation, we design an algorithm to enumerate all semi-balanced colorings of G in O(nm(2)) time.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Graphs and Combinatorics
volume
20
issue
2
pages
205 - 222
publisher
Springer
external identifiers
  • wos:000221884700006
  • scopus:4544357741
ISSN
0911-0119
DOI
10.1007/s00373-004-0557-0
language
English
LU publication?
yes
id
a3dd66f9-a030-4339-ac4f-598f88eaef89 (old id 275306)
date added to LUP
2007-10-23 11:11:04
date last changed
2017-08-13 04:13:54
@article{a3dd66f9-a030-4339-ac4f-598f88eaef89,
  abstract     = {We generalize the concept of a 2-coloring of a graph to what we call a semi-balanced coloring by relaxing a certain discrepancy condition on the shortest-paths hypergraph of the graph. Let G be an undirected, unweighted, connected graph with n vertices and m edges. We prove that the number of different semi-balanced colorings of G is: (1) at most n+1 if G is bipartite; (2) at most m if G is non-bipartite and triangle-free; and (3) at most m+1 if G is non-bipartite. Based on the above combinatorial investigation, we design an algorithm to enumerate all semi-balanced colorings of G in O(nm(2)) time.},
  author       = {Jansson, Jesper and Tokuyama, T},
  issn         = {0911-0119},
  language     = {eng},
  number       = {2},
  pages        = {205--222},
  publisher    = {Springer},
  series       = {Graphs and Combinatorics},
  title        = {Semi-balanced colorings of graphs: Generalized 2-colorings based on a relaxed discrepancy condition},
  url          = {http://dx.doi.org/10.1007/s00373-004-0557-0},
  volume       = {20},
  year         = {2004},
}