Long Paths in the Distance Graph over Large Subsets of Vector Spaces over Finite Fields

David Covert; Michael Bennett; Jonathan Chapman; Derrick Hart; Alex Iosevichc; Jonathan Pakianathan

doi:10.4134/JKMS.2016.53.1.115

Long Paths in the Distance Graph over Large Subsets of Vector Spaces over Finite Fields

David Covert, Michael Bennett, Jonathan Chapman, Derrick Hart, Alex Iosevichc, Jonathan Pakianathan

University of Missouri-St. Louis

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

Abstract

<div class="line" id="line-5"> Let E⊂Fdq, the d-dimensional vector space over a finite field with q elements. Construct a graph, called the distance graph of E, by letting the vertices be the elements of E and connect a pair of vertices corresponding to vectors x,y∈E by an edge if ||x−y||=(x1−y1)2+&ctdot;+(xd−yd)2=1. We shall prove that if the size of E is sufficiently large, then the distance graph of E contains long non-overlapping paths and vertices of high degree.</div>

Original language	American English
Journal	Journal of the Korean Mathematical Society
Volume	53
DOIs	https://doi.org/10.4134/JKMS.2016.53.1.115
State	Published - May 31 2014

Disciplines

Computer Sciences
Mathematics

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Cite this

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title = "Long Paths in the Distance Graph over Large Subsets of Vector Spaces over Finite Fields",

abstract = " Let E⊂Fdq, the d-dimensional vector space over a finite field with q elements. Construct a graph, called the distance graph of E, by letting the vertices be the elements of E and connect a pair of vertices corresponding to vectors x,y∈E by an edge if ||x−y||=(x1−y1)2+&ctdot;+(xd−yd)2=1. We shall prove that if the size of E is sufficiently large, then the distance graph of E contains long non-overlapping paths and vertices of high degree.",

author = "David Covert and Michael Bennett and Jonathan Chapman and Derrick Hart and Alex Iosevichc and Jonathan Pakianathan",

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AU - Bennett, Michael

AU - Chapman, Jonathan

AU - Hart, Derrick

AU - Iosevichc, Alex

AU - Pakianathan, Jonathan

PY - 2014/5/31

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N2 - Let E⊂Fdq, the d-dimensional vector space over a finite field with q elements. Construct a graph, called the distance graph of E, by letting the vertices be the elements of E and connect a pair of vertices corresponding to vectors x,y∈E by an edge if ||x−y||=(x1−y1)2+&ctdot;+(xd−yd)2=1. We shall prove that if the size of E is sufficiently large, then the distance graph of E contains long non-overlapping paths and vertices of high degree.

AB - Let E⊂Fdq, the d-dimensional vector space over a finite field with q elements. Construct a graph, called the distance graph of E, by letting the vertices be the elements of E and connect a pair of vertices corresponding to vectors x,y∈E by an edge if ||x−y||=(x1−y1)2+&ctdot;+(xd−yd)2=1. We shall prove that if the size of E is sufficiently large, then the distance graph of E contains long non-overlapping paths and vertices of high degree.

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DO - 10.4134/JKMS.2016.53.1.115

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JO - Journal of the Korean Mathematical Society

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