Vol. 11, No. 1, 2018

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On halving-edges graphs

Tanya Khovanova and Dai Yang

Vol. 11 (2018), No. 1, 1–11
DOI: 10.2140/involve.2018.11.1
Abstract

In this paper we study halving-edges graphs corresponding to a set of halving lines. Particularly, we study the vertex degrees, path, cycles and cliques of such graphs. In doing so, we study a vertex-partition of said graph called chains which are equipped with interesting properties.

Keywords
combinatorics, halving lines, combinatorial geometry, discrete math
Mathematical Subject Classification 2010
Primary: 05C30
Milestones
Received: 28 April 2013
Revised: 28 September 2014
Accepted: 17 October 2016
Published: 17 July 2017

Communicated by Kenneth S. Berenhaut
Authors
Tanya Khovanova
Department of Mathematics
MIT
77 Massachusetts Ave
Cambridge, MA 20139
United States
Dai Yang
Department of Mathematics
MIT
575 S Rengstorff
Mountain View, CA 94040
United States