- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnline Submission ㆍMy Manuscript - For Reviewers - For Editors
 Embedding distance graphs in finite field vector spaces J. Korean Math. Soc. 2019 Vol. 56, No. 6, 1515-1528 https://doi.org/10.4134/JKMS.j180776Published online November 1, 2019 Alex Iosevich, Hans Parshall University of Rochester; The Ohio State University Abstract : We show that large subsets of vector spaces over finite fields determine certain point configurations with prescribed distance structure. More specifically, we consider the complete graph with vertices as the points of $A \subseteq \mathbf{F}_q^d$ and edges assigned the algebraic distance between pairs of vertices. We prove nontrivial results on locating specified subgraphs of maximum vertex degree at most $t$ in dimensions $d \geq 2t$. Keywords : Erd\H{o}s distance problem, finite fields, graph theory MSC numbers : 52C10, 11T23 Downloads: Full-text PDF   Full-text HTML