Partition dimension of projective planes

Zolt\'an Bl\'azsik; Zolt\'an L\'or\'ant Nagy

arXiv:1611.09637·math.CO·November 30, 2016·Eur. J. Comb.

Partition dimension of projective planes

Zolt\'an Bl\'azsik, Zolt\'an L\'or\'ant Nagy

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TL;DR

This paper investigates the partition dimension of the incidence graph of a projective plane, establishing bounds proportional to the logarithm of the order of the plane, thus advancing understanding of graph partitioning in combinatorics.

Contribution

It provides tight bounds on the partition dimension of the incidence graph of projective planes, a significant step in combinatorial graph theory.

Findings

01

Partition dimension is proportional to log(q)

02

Bounds are established within a factor of 2

03

Results apply to the incidence graph of projective planes

Abstract

We determine the partition dimension of the incidence graph $G (Π_{q})$ of the projective plane $Π_{q}$ up to a constant factor $2$ as $(2 + o (1)) lo g_{2} q \leq pd (G (Π_{q})) \leq (4 + o (1)) lo g_{2} q .$

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Taxonomy

TopicsGraph Labeling and Dimension Problems · graph theory and CDMA systems · Finite Group Theory Research