7 papers
Removable trees and matchings in -connected and -edge-connected graphs
Adam D. W. Clay, Tibor Jordán, Tibor Jordán
T. Hasunuma (J. Graph Theory, 2023) conjectured that if is a -connected (resp. -edge-connected) graph with minimum degree , and is a tree of order…
Characterizing globally linked pairs in graphs
Tibor Jordán, Shin-ichi Tanigawa
A pair of vertices is said to be globally linked in a -dimensional framework if there exists no other framework with the same edge lengths, in which th…
Sufficient conditions for bipartite rigidity, symmetric completability and hyperconnectivity of graphs
Dániel Garamvölgyi, Bill Jackson, Tibor Jordán +1
We consider three matroids defined by Kalai in 1985: the symmetric completion matroid on the edge set of a looped complete graph; the hyperconnectivity matroid $\ma…
Degree Sum Conditions for Graph Rigidity
Tibor Jordán, Xuemei Liu, Soma Villányi
We study sufficient conditions for the generic rigidity of a graph expressed in terms of (i) its minimum degree , or (ii) the parameter $η(G)=\min_{uv\notin E}(°(u)+°…
Sparsity, Stress-Independence and Globally Linked Pairs in Graph Rigidity Theory
Dániel Garamvölgyi, Bill Jackson, Tibor Jordán
A graph is -independent (resp. -connected) if its -dimensional generic rigidity matroid is free (resp. connected). A result of Maxwell from 1867 im…
Rigidity of Graphs and Frameworks: A Matroid Theoretic Approach
James Cruickshank, Bill Jackson, Tibor Jordán +1
A -dimensional (bar-and-joint) framework consists of a graph and a realisation . It is rigid if every continuous motion of the vertices wh…