Unified bounds for the independence number of graph powers

Fuente: arXiv
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Main Authors: Abiad, Aida, Zhou, Jiang
Format: Preprint
Published: 2024
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author Abiad, Aida
Zhou, Jiang
author_facet Abiad, Aida
Zhou, Jiang
contents For a graph $G$, its $k$-th power $G^k$ is constructed by placing an edge between two vertices if they are within distance $k$ of each other. The $k$-independence number $α_k(G)$ is defined as the independence number of $G^k$. By using general semidefinite programming and polynomial methods, we derive sharp bounds for the $k$-independence number of a graph, which extend and unify various existing results. Our work also allows us to easily derive some new bounds for $α_k(G)$.
format Preprint
id arxiv_https___arxiv_org_abs_2411_09450
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Unified bounds for the independence number of graph powers
Abiad, Aida
Zhou, Jiang
Combinatorics
For a graph $G$, its $k$-th power $G^k$ is constructed by placing an edge between two vertices if they are within distance $k$ of each other. The $k$-independence number $α_k(G)$ is defined as the independence number of $G^k$. By using general semidefinite programming and polynomial methods, we derive sharp bounds for the $k$-independence number of a graph, which extend and unify various existing results. Our work also allows us to easily derive some new bounds for $α_k(G)$.
title Unified bounds for the independence number of graph powers
topic Combinatorics
url https://arxiv.org/abs/2411.09450