2 citations · 3 across the 7 of their papers we have counts for
7 papers
k-connected degree sequences
Jonathan McLaughlin
Necessary and sufficient conditions for a sequence of positive integers to be the degree sequence of a k-connected simple graph are detailed. Conditions are also given under which…
3-connected graphs and their degree sequences
Jonathan McLaughlin
Necessary and sufficient conditions for a sequence of positive integers to be the degree sequence of a 3-connected simple graph are detailed. Conditions are also given under which…
On connected simple graphs and their degree sequences
Jonathan McLaughlin
This note describes necessary and sufficient conditions for a sequence of positive integers to be the degree sequence of a connected simple graph. Conditions are also given under w…
On connected degree sequences
Jonathan McLaughlin
This note gives necessary and sufficient conditions for a sequence of non-negative integers to be the degree sequence of a connected simple graph. This result is implicit in a pape…
Constructing 2- and 3-connected graphs
Jonathan McLaughlin
This work re-examines a classical construction of a 2-connected (simple) graph where every intermediate graph is 2-connected before detailing an analogous construction for 3-connec…
The Realizable Extension Problem and the Weighted Graph
Jonathan McLaughlin
This note outlines the realizable extension problem for weighted graphs and provides results of a detailed analysis of this problem for the weighted graph . This analy…
Series Parallel Linkages
James Cruickshank, Jonathan McLaughlin
We study spaces of realisations of linkages (weighted graphs) whose underlying graph is a series parallel graph. In particular, we describe an algorithm for determining whether or…