12 citations · 23 across the 12 of their papers we have counts for
12 papers
Primality of theta-curves with proper rational tangle unknotting number one
Kenneth L. Baker, Dorothy Buck, Danielle O'Donnol +2
We show that if a composite -curve has (proper rational) unknotting number one, then it is the order 2 sum of a (proper rational) unknotting number one knot and a trivial -cu…
Unknotting numbers for prime -curves up to seven crossings
Dorothy Buck, Danielle O'Donnol
Determining unknotting numbers is a large and widely studied problem. We consider the more general question of the unknotting number of a spatial graph. We show the unknotting numb…
Planar Legendrian -graphs
Peter Lambert-Cole, Danielle O'Donnol
We classify topologically trivial Legendrian -graphs and identify the complete family of nondestabilizeable Legendrian realizations in this topological class. In contrast to all…
Planar Legendrian graphs
Peter Lambert-Cole, Danielle O'Donnol
We prove two results on the classification of trivial Legendrian embeddings of planar graphs. First, the oriented Legendrian ribbon and rotat…
The total Thurston-Bennequin number of complete and complete bipartite Legendrian graphs
Danielle O'Donnol, Elena Pavelescu
We study the Thurston-Bennequin number of complete and complete bipartite Legendrian graphs. We define a new invariant called the total Thurston-Bennequin number of the graph. We s…
Heegaard Floer homology of spatial graphs
Shelly Harvey, Danielle O'Donnol
We extend the theory of combinatorial link Floer homology to a class of oriented spatial graphs called transverse spatial graphs. To do this, we define the notion of a grid diagram…
Intrinsic 3-linkedness is Not Preserved by moves
Danielle O'Donnol
This paper introduces a number of new intrinsically 3-linked graphs through five new constructions. We then prove that intrinsic 3-linkedness is not preserved by m…
An application of topological graph clustering to protein function prediction
R. Sean Bowman, Douglas Heisterkamp, Jesse Johnson +1
We use a semisupervised learning algorithm based on a topological data analysis approach to assign functional categories to yeast proteins using similarity graphs. This new approac…
Legendrian theta-graphs
Danielle O'Donnol, Elena Pavelescu
In this article we give necessary and sufficient conditions for two triples of integers to be realized as the Thurston-Bennequin number and the rotation number of a Legendrian thet…
On Legendrian Graphs
Danielle O'Donnol, Elena Pavelescu
We investigate Legendrian graphs in . We extend the classical invariants, Thurston-Bennequin number and rotation number to Legendrian graphs. We prove that a graph…
Knotting and linking in the Petersen family
Danielle O'Donnol
This paper focuses on the graphs in the Petersen family, the set of minor minimal intrinsically linked graphs. We prove there is a relationship between algebraic linking of an embe…
Intrinsically n-linked Complete Bipartite Graphs
Danielle O'Donnol
We prove that every embedding of into contains a non-split link of -components. Further, given an embedding of in , every edge of $K…