TY - JOUR
AU1 - Chudnovsky, Maria
AU2 - Schaudt, Oliver
AU3 - Spirkl, Sophie
AU4 - Stein, Maya
AU5 - Zhong, Mingxian
AB - It is an open problem whether the 3-coloring problem can be solved in polynomial time in the class of graphs that do not contain an induced path on t vertices, for fixed t. We propose an algorithm that, given a 3-colorable graph without an induced path on t −1 t vertices, computes a coloring with max 5, 2 − 2 many colors. If the input t −1 graph is triangle-free, we only need max 4, + 1 many colors. The running t −2 2 time of our algorithm is O((3 + t )m + n) if the input graph has n vertices and m edges. Keywords Graph coloring · Forbidden induced paths · Approximation algorithm Mathematics Subject Classification 05C69 · 05C75 · 05C38 An extended abstract of the paper has previously appeared in Bodlaender H., Woeginger G. (eds): Graph-Theoretic Concepts in Computer Science (WG) 2017. Lecture Notes in Computer Science, vol 10520. Springer, Cham. The first author was supported by National Science Foundation grant DMS-1550991 and US Army Research Office Grant W911NF-16-1-0404. The fourth author was supported by Fondecyt Grants 1140766 and 1180830, by CMM-Basal AFB 170001, and by Millennium Nucleus Information and Coordination in Networks. B Sophie Spirkl 
TI - Approximately Coloring Graphs Without Long Induced Paths
JF - Algorithmica
DO - 10.1007/s00453-019-00577-6
DA - 2019-04-26
UR - https://www.deepdyve.com/lp/springer-journals/approximately-coloring-graphs-without-long-induced-paths-6HMQQuiuKB
SP - 1
EP - 14
VL - OnlineFirst
IS - 
DP - DeepDyve
ER -