Abstract
We study inverse chromatic number problems in permutation graphs and in interval graphs. Given a fixed instance and a fixed integer K, the instance has to be modified as little as possible so that the newly obtained graph can be colored with K colors or less. We show that the inverse (p, k)-colorability problem (defined similarly) in permutation graphs is polynomially solvable for fixed p and k. We then propose a polynomial-time algorithm for solving inverse chromatic number problem in interval graphs where all intervals have length 1 or 2. We also show that the latter problem is NP-hard if there is a constant number of different interval lengths.
| Original language | English |
|---|---|
| Pages (from-to) | 1129-1136 |
| Number of pages | 8 |
| Journal | Electronic Notes in Discrete Mathematics |
| Volume | 36 |
| Issue number | C |
| DOIs | |
| Publication status | Published - 2010 Aug 1 |
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All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics
- Applied Mathematics
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On inverse chromatic number problems (Extended abstract). / Chung, Yerim; Culus, Jean François; Demange, Marc.
In: Electronic Notes in Discrete Mathematics, Vol. 36, No. C, 01.08.2010, p. 1129-1136.Research output: Contribution to journal › Article
TY - JOUR
T1 - On inverse chromatic number problems (Extended abstract)
AU - Chung, Yerim
AU - Culus, Jean François
AU - Demange, Marc
PY - 2010/8/1
Y1 - 2010/8/1
N2 - We study inverse chromatic number problems in permutation graphs and in interval graphs. Given a fixed instance and a fixed integer K, the instance has to be modified as little as possible so that the newly obtained graph can be colored with K colors or less. We show that the inverse (p, k)-colorability problem (defined similarly) in permutation graphs is polynomially solvable for fixed p and k. We then propose a polynomial-time algorithm for solving inverse chromatic number problem in interval graphs where all intervals have length 1 or 2. We also show that the latter problem is NP-hard if there is a constant number of different interval lengths.
AB - We study inverse chromatic number problems in permutation graphs and in interval graphs. Given a fixed instance and a fixed integer K, the instance has to be modified as little as possible so that the newly obtained graph can be colored with K colors or less. We show that the inverse (p, k)-colorability problem (defined similarly) in permutation graphs is polynomially solvable for fixed p and k. We then propose a polynomial-time algorithm for solving inverse chromatic number problem in interval graphs where all intervals have length 1 or 2. We also show that the latter problem is NP-hard if there is a constant number of different interval lengths.
UR - http://www.scopus.com/inward/record.url?scp=77954949804&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77954949804&partnerID=8YFLogxK
U2 - 10.1016/j.endm.2010.05.143
DO - 10.1016/j.endm.2010.05.143
M3 - Article
AN - SCOPUS:77954949804
VL - 36
SP - 1129
EP - 1136
JO - Electronic Notes in Discrete Mathematics
JF - Electronic Notes in Discrete Mathematics
SN - 1571-0653
IS - C
ER -