Linear Eulerian Extensions of Inhomogenous Random Graphs
Probability
2023-05-15 v1 Combinatorics
Abstract
The Eulerian extension number of any graph~ (i.e. the minimum number of edges needed to be added to make~ Eulerian) is at least~ half the number of odd degree vertices of~ In this paper we consider an inhomogenous random graph~ whose edge probabilities need not all be the same and use an iterative probabilistic method to obtain sufficient conditions for the Eulerian extension number of~ to grow \emph{linearly} with~ We derive our conditions in terms of the average edge probabilities and edge density and also briefly illustrate our result with an example.
Cite
@article{arxiv.2305.07137,
title = {Linear Eulerian Extensions of Inhomogenous Random Graphs},
author = {Ghurumuruhan Ganesan},
journal= {arXiv preprint arXiv:2305.07137},
year = {2023}
}