7 papers · 1 filter
The property: a bridge between split graphs and Number Theory
Victor N. Schvöllner
For a split graph , the combinatorics of 2-switches on is faithfully encoded by the factor graph , a multigraph whose induced cycles have length at most . In this p…
Induced paths and cycles in factor graphs of split graphs
Victor N. Schvöllner, Adrián Pastine
Let be a split graph with bipartition and let be the factor graph associated with , a multigraph on whose encodes the combinatorial information about 2-sw…
2-switch: transition and stability on forests and pseudofests
Victor N. Schvöllner, Adrián Pastine, Daniel A. Jaume
Given any two forests (pseudoforests) with the same degree sequence, we show that one can be transformed into the other by a sequence of 2-switches in such a way that all the inter…
Simple factor graphs associated with split graphs
Victor Nicolas Schvöllner, Adrian Pastine
We introduce and study a loopless multigraph associated with a split graph : its factor graph , whose vertex set is and whose edges, counted with multiplicit…
2-switch-degree classification of split graphs
Victor Nicolas Schvöllner
The 2-switch-degree of is the number of distinct 2-switches acting on a graph . In this work we study structural properties of the 2-switch-degree, with a focus on split gra…
2-switch transition on unicyclic graphs and pseudoforest
Daniel A. Jaume, Adrián Pastine, Victor Schvöllner
In the present work we prove that given any two unicycle graphs (pseudoforests) that share the same degree sequence there is a finite sequence of 2-switches transforming one into t…