The closed neighborhood conflict-free chromatic number of a graph (Formula presented.), denoted by (Formula presented.), is the minimum number of colors required to color the vertices of (Formula presented.) such that for every vertex, there is a color that appears exactly once in its closed neighborhood. Pach and Tardos showed that (Formula presented.), for any (Formula presented.), where (Formula presented.) is the maximum degree. In 2014, Glebov et al. showed existence of graphs (Formula presented.) with (Formula presented.). In this article, we bridge the gap between the two bounds by showing that (Formula presented.). © 2021 Wiley Periodicals LLC

Subrahmanyam Kalyanasundaram

Department of Computer Science and Engineering

Rogers Mathew

S. Bhyravarapu

Fulltext

Indian Institute of Technology Hyderabad (IITH) is a premier institute of science and technology established in 2008. IITH has been consistently ranked in the&nbsp;<a href="https://iith.ac.in/reports/" rel="noopener noreferrer">top 10 institutes</a>&nbsp;in India for Engineering&nbsp;<a href="https://www.nirfindia.org/2021/EngineeringRanking.html" rel="noopener noreferrer" target="_blank">according to NIRF</a>&nbsp;making it one of the most coveted schools for science and technology in the country.

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Journal	Data powered by TypesetJournal of Graph Theory
Publisher	Data powered by TypesetJohn Wiley and Sons Inc
ISSN	03649024