Chromatic Bounds for Some Subclasses of $$(P_3\cup P_2)$$-free graphs

Prashant, Athmakoori; Francis, Philip H.; Raj, S. Francis

doi:10.1007/978-3-030-95018-7_2

Cited by 3 publications

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“…There have been extensive studies to find linear subfamilies even for various superclasses of 2K 2 -free graphs. See for instance [1,2,6,10,11,13]. One of the superclass of 2K 2 -free graphs studied is the class of (P 3 ∪ P 2 )-free graphs.…”

Section: Gyárfás Posed a Lot Of Open Problems And Conjectures Which S...mentioning

confidence: 99%

“…Choudum gave a χ-binding function of O(ω 3 ) for the class of (P 3 ∪ P 2 )-free graphs and obtained a special linear χ-binding function for {P 3 ∪ P 2 , diamond}-free graphs. A. Prashant et al in [10], have shown that {P 3 ∪ P 2 , 2K 1 + K p }-free graphs and {P 3 ∪ P 2 , (K 1 ∪ K 2 ) + K p }-free graphs admit a linear χ-binding function. In [4], S. A. Choudum et al gave a decomposition theorem for {P 3 ∪ P 2 , C 4 }-free graphs and as a result showed that f * = 5ω 4 .…”

Section: Gyárfás Posed a Lot Of Open Problems And Conjectures Which S...mentioning

confidence: 99%

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Chromatic Bounds for the Subclasses of $$pK_2$$-Free Graphs

Prashant

Gokulnath

2021

Algorithms and Discrete Applied Mathematics

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Finding families that admit a linear χ-binding function is a problem that has interested researchers for a long time. Recently, the question of finding linear subfamilies of 2K 2 -free graphs has garnered much attention. In this paper, we are interested in finding a linear subfamily of a specific superclass of 2K 2 -free graphs, namely (P 3 ∪ P 2 )-free graphs. We show that the class of {P 3 ∪ P 2 , gem}-free graphs admits f = 2ω as a linear χ-binding function.Furthermore, we give examples to show that the optimal χ-binding function f * ≥ 5ω(G) 4 for the class of {P 3 ∪ P 2 , gem}-free graphs and that the χ-binding function f = 2ω is tight when ω = 2 and 3.

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