A note on "Folding wheels and fans."
Ton Kloks, Yue-Li Wang
TL;DR
This paper critiques existing formulas for clique numbers in folding wheels and fans, introduces a generalized interpolation theorem, corrects a previous formula for wheels, and explores properties of threshold graphs related to folding and chromatic numbers.
Contribution
It presents a generalized interpolation theorem, corrects a prior formula for wheels, and analyzes folding and chromatic numbers in threshold graphs.
Findings
The existing formula for wheels is incorrect.
A new interpolation theorem generalizes previous results.
In threshold graphs, folding number equals chromatic number.
Abstract
In S.Gervacio, R.Guerrero and H.Rara, Folding wheels and fans, Graphs and Combinatorics 18 (2002) 731-737, the authors obtain formulas for the clique numbers onto which wheels and fans fold. We present an interpolation theorem which generalizes their theorems 4.2 and 5.2. We show that their formula for wheels is wrong. We show that for threshold graphs, the achromatic number and folding number coincides with the chromatic number.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Graph Theory Research · Limits and Structures in Graph Theory