Quadratic Embedding of Theta Graphs via Reproducing Kernel Hilbert Spaces

TL;DR

This paper characterizes the quadratic embedding property of theta graphs using reproducing kernel Hilbert space techniques, providing an alternative proof to a known theorem by Winkler (1985).

Contribution

It introduces an RKHS-based proof for the quadratic embedding characterization of theta graphs, offering a new perspective on the existing theorem.

Findings

Complete characterization of quadratic embedding for theta graphs

Alternative proof using RKHS techniques

Connection to Winkler's 1985 theorem

Abstract

The quadratic embedding property of graphs consisting of three paths (theta graphs) is fully characterised. For this aim, a theorem by Winkler (1985) is utilized. An alternative proof of that result using the RKHS technique is presented.