What question did this study set out to answer?

The research aims to establish the existence of claw-decomposition in the generalized Kneser graph GKGn,3,1 for larger values of n.

February 9, 2026Open Access

Claw-decomposition of generalized Kneser graph GKGn,3,1

Key Points

The research aims to establish the existence of claw-decomposition in the generalized Kneser graph GKGn,3,1 for larger values of n.
Defined claw as a star with three edges.
Introduced the structure of Generalized Kneser Graph GKGn,k,r.
Demonstrated adjacency based on intersection properties of k-element subsets.
Proven claw-decomposition exists for GKGn,3,1 when n is 6 or greater.

Abstract

A star with three edges is called a claw. The Generalized Kneser Graph GKGn,k,r is the graph whose vertices are the k-element subsets of n-elements, in which two vertices are adjacent if and only if they intersect in precisely r elements. In this paper, we prove that the graph GKGn,3,1 has a claw-decomposition for all n ? 6.

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Cite This Study

Arthi et al. (Wed,) studied this question.

synapsesocial.com/papers/698979b9f0ec2af6756e7984 https://doi.org/https://doi.org/10.2298/fil2516733a

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