On graphs and algebraic graphs that do not contain cycles of length 4

Noga Alon; H. Tracy Hall; Christian Knauer; Rom Pinchasi; Raphael Yuster

doi:10.1002/jgt.20542

On graphs and algebraic graphs that do not contain cycles of length 4

Noga Alon^*, H. Tracy Hall, Christian Knauer, Rom Pinchasi, Raphael Yuster

^*Corresponding author for this work

School of Computer Science

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We consider extremal problems for algebraic graphs, that is, graphs whose vertices correspond to vectors in ℝ^d, where two vectors are connected by an edge according to an algebraic condition. We also derive a lower bound on the rank of the adjacency matrix of a general abstract graph using the number of 4-cycles and a parameter which measures how close the graph is to being regular. From this, we derive a rank bound for the adjacency matrix A of any simple graph with n vertices and E edges which does not contain a copy of.

Original language	English
Pages (from-to)	91-102
Number of pages	12
Journal	Journal of Graph Theory
Volume	68
Issue number	2
DOIs	https://doi.org/10.1002/jgt.20542
State	Published - Oct 2011

Keywords

adjacency rank
algebraic graph
bipartite
forbidden subgraph
graph regularity
minimum rank
multiset regularity
square-avoiding
square-free

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10.1002/jgt.20542

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abstract = "We consider extremal problems for algebraic graphs, that is, graphs whose vertices correspond to vectors in ℝd, where two vectors are connected by an edge according to an algebraic condition. We also derive a lower bound on the rank of the adjacency matrix of a general abstract graph using the number of 4-cycles and a parameter which measures how close the graph is to being regular. From this, we derive a rank bound for the adjacency matrix A of any simple graph with n vertices and E edges which does not contain a copy of.",

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AU - Hall, H. Tracy

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AU - Yuster, Raphael

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KW - adjacency rank

KW - algebraic graph

KW - bipartite

KW - forbidden subgraph

KW - graph regularity

KW - minimum rank

KW - multiset regularity

KW - square-avoiding

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On graphs and algebraic graphs that do not contain cycles of length 4

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