Zobrazeno 1 - 10
of 104
pro vyhledávání: '"Mattman, Thomas W"'
Autor:
Barnett, Andrea, Bond, Robert, Macias, Anthony, Mattman, Thomas W., Parnell, Bill, Schoenfield, Ely
We use Hartnell's model for virus spread on a graph, also known as firefighting. For rooted trees, we propose an Unburning Algorithm, a type of greedy algorithm starting from the leaves and working back towards the root. We show that the algorithm sa
Externí odkaz:
http://arxiv.org/abs/2409.14303
Autor:
Ichihara, Kazuhiro, Mattman, Thomas W.
For a hyperbolic knot in $S^3$, Dehn surgery along slope $r \in \Q \cup \{\frac10\}$ is {\em exceptional} if it results in a non-hyperbolic manifold. We say meridional surgery, $r = \frac10$, is {\em trivial} as it recovers the manifold $S^3$. We pro
Externí odkaz:
http://arxiv.org/abs/2309.09918
We show, for every positive integer $n$, there is an alternating knot having a boundary slope with denominator $n$. We make use of Kabaya's method for boundary slopes and the layered solid torus construction introduced by Jaco and Rubinstein and furt
Externí odkaz:
http://arxiv.org/abs/2309.02370
Autor:
Kim, Hyoungjun, Mattman, Thomas W.
The Graph Minor Theorem of Robertson and Seymour implies a finite set of obstructions for any minor closed graph property. We show that there are only three obstructions to knotless embedding of size 23, which is far fewer than the 92 of size 22 and
Externí odkaz:
http://arxiv.org/abs/2205.14255
A graph is intrinsically knotted if every embedding contains a nontrivially knotted cycle. It is known that intrinsically knotted graphs have at least 21 edges and that there are exactly 14 intrinsically knotted graphs with 21 edges, in which the Hea
Externí odkaz:
http://arxiv.org/abs/2205.06199
Autor:
Kim, Hyoungjun, Mattman, Thomas W.
Publikováno v:
In Discrete Applied Mathematics 15 January 2025 360:139-166
Publikováno v:
Algebr. Geom. Topol. 24 (2024) 1203-1223
It has been an open question whether the deletion or contraction of an edge in an intrinsically knotted graph always yields an intrinsically linked graph. We present a new intrinsically knotted graph that shows the answer to both questions is no.
Externí odkaz:
http://arxiv.org/abs/2111.08859
Publikováno v:
Algebr. Geom. Topol. 23 (2023) 1831-1848
A graph is maximal knotless if it is edge maximal for the property of knotless embedding in $R^3$. We show that such a graph has at least $\frac74 |V|$ edges, and construct an infinite family of maximal knotless graphs with $|E| < \frac52|V|$. With t
Externí odkaz:
http://arxiv.org/abs/2101.05241
Publikováno v:
Involve 15 (2022) 669-686
The obstruction set for graphs with knotless embeddings is not known, but a recent paper of Goldberg, Mattman, and Naimi indicates that it is quite large. Almost all known obstructions fall into four Triangle-Y families and they ask if there is an ef
Externí odkaz:
http://arxiv.org/abs/2008.12975
We show that, for an alternating knot, the ratio of the diameter of the set of boundary slopes to the crossing number can be arbitrarily large.
Comment: 10 pages, 9 figures
Comment: 10 pages, 9 figures
Externí odkaz:
http://arxiv.org/abs/1911.08562