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A linear upper bound on the number of moves required for independent set reconfiguration with two sliding tokens · arXivDesk

2608.13130Aug 13, 202610 pages, 2 figures

A linear upper bound on the number of moves required for independent set reconfiguration with two sliding tokens

Nived J. M., Mathew C. Francis

Combinatorics Discrete Mathematics

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Abstract

We consider the problem of shifting two tokens placed on nonadjacent vertices $u,v$ of a graph $G$ on $n$ vertices to two nonadjacent vertices $u',v'$

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We consider the problem of shifting two tokens placed on nonadjacent vertices u,v of a graph G on n vertices to two nonadjacent vertices u',v' of G using a sequence of token movements. In each step, a token is moved from the vertex it is on to a neighbour of that vertex, ensuring that the tokens remain on nonadjacent vertices after this move.

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The paper addresses: A linear upper bound on the number of moves required for independent set reconfiguration with two sliding tokens.
We consider the problem of shifting two tokens placed on nonadjacent vertices u,v of a graph G on n vertices to two nonadjacent vertices u',v' of G using a sequence of token movements.