Perfectly colorable graphs

• Published in: Information processing letters Vol. 111; no. 19; pp. 960 - 961
• Main Author: Sandeep, R.B.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 15-10-2011; Elsevier; Elsevier Sequoia S.A
• Subjects: Algorithmics. Computability. Computer arithmetics; Applied sciences; Coloring; Combinatorial problems; Combinatorics; Combinatorics. Ordered structures; Computer science; control theory; systems; Exact sciences and technology; Graph coloring; Graph theory; Graphs; Information retrieval. Graph; Mathematics; Miscellaneous; Optimization algorithms; Perfect coloring; Perfect graphs; Perfect paw-free graphs; Perfectly colorable graphs; Recognition; Sciences and techniques of general use; Studies; Theoretical computing; Perfectly colorable graphs; Combinatorial problems; Perfect coloring; Perfect paw-free graphs; Perfect graphs; Computer theory; Combinatorial problem; Color; Linear time; Information processing; Subgraph; Graph colouring; Algorithm analysis
• ISSN: 0020-0190; 1872-6119
• DOI: 10.1016/j.ipl.2011.07.001

We define a
perfect coloring of a graph
G as a proper coloring of
G such that every connected induced subgraph
H of
G uses exactly
ω
(
H
)
many colors where
ω
(
H
)
is the clique number of
H. A graph is
perfectly colorable if it admits a perfect coloring. We show that the class of perfectly colorable graphs is exactly the class of perfect paw-free graphs. It follows that perfectly colorable graphs can be recognized and colored in linear time.
► We define a new type of vertex coloring. ► We also define a new class of graphs based on that coloring. ► We characterize the new class of graphs. ► There exist linear time algorithms for recognizing and coloring these graphs.