Extremal results for graphs of bounded metric dimension
نویسندگان
چکیده
Metric dimension is a graph parameter motivated by problems in robot navigation, drug design, and image processing. In this paper, we answer several open extremal on metric pattern avoidance graphs from Geneson (2020). Specifically, construct new family of that allows us to determine the maximum possible degree at most k, degeneracy chromatic number n for which there exists k contains Kn,n. We also investigate variant called edge solve another problem same paper sufficiently large showing Pnd d n≥dd−1. addition, use probabilistic argument make progress clique 2Θ(k). Zubrilina (2018) finding triples (x,y,n) x, y, order n. particular, show each integer k>0, exist G with 3k(1−o(1)), 3k(1+o(1)).
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2022
ISSN: ['1872-6771', '0166-218X']
DOI: https://doi.org/10.1016/j.dam.2021.11.015