Zobrazeno 1 - 10
of 22
pro vyhledávání: '"Thomas W. Mattman"'
Publikováno v:
Characters in Low-Dimensional Topology. :207-216
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.
10 pages, 9 figures
10 pages, 9 figures
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::881ebd16b9d88b7ebabeac5e1d5ef8a5
https://doi.org/10.1090/conm/760/15292
https://doi.org/10.1090/conm/760/15292
Publikováno v:
Topology and its Applications. 228:303-317
A graph is called intrinsically knotted if every embedding of the graph contains a knotted cycle. Johnson, Kidwell, and Michael showed that intrinsically knotted graphs have at least 21 edges. Recently Lee, Kim, Lee and Oh (and, independently, Barsot
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0d1717f10fd01103a41b978a6c495419
https://doi.org/10.1016/j.topol.2017.06.013
https://doi.org/10.1016/j.topol.2017.06.013
We show that two-bridge knots and alternating fibered knots admit no purely cosmetic surgeries, i.e., no pair of distinct Dehn surgeries on such a knot produce 3-manifolds that are homeomorphic as oriented manifolds. Our argument, based on a recent r
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8f58ff0a3df3477caa7b32b184a15faf
http://arxiv.org/abs/1909.02340
http://arxiv.org/abs/1909.02340
Publikováno v:
Journal of Graph Theory. 85:568-584
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 the KS graphs, K7 and the 13 graphs obtained from K7 by ∇Y moves, are the only
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::490f66710655c2e105fa32903cc5ad5f
https://doi.org/10.1002/jgt.22091
https://doi.org/10.1002/jgt.22091
We determine p-colorability of the paradromic rings. These rings arise by generalizing the well-known experiment of bisecting a Mobius strip. Instead of joining the ends with a single half twist, use $m$ twists, and, rather than bisecting ($n = 2$),
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::51a44d3eb6f801d2e89032830e244861
Fleming and Foisy recently proved the existence of a digraph whose every embedding contains a $4$-component link, and left open the possibility that a directed graph with an intrinsic $n$-component link might exist. We show that, indeed, this is the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::50eb7a8cf0b4d15800aacd85c63ce2e9
Autor:
Kazuhiro Ichihara, Thomas W. Mattman
We present four models for a random graph and show that, in each case, the probability that a graph is intrinsically knotted goes to one as the number of vertices increases. We also argue that, for $k \geq 18$, most graphs of order $k$ are intrinsica
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::30664fa92cf685c6e8a8f55589cd858e
http://arxiv.org/abs/1811.09726
http://arxiv.org/abs/1811.09726
Autor:
Thomas W. Mattman
Publikováno v:
Foundations for Undergraduate Research in Mathematics ISBN: 9783319660646
The Graph Minor Theorem of Robertson and Seymour associates, to any graph property whatsoever, a finite, characteristic list of graphs. We view this as an impressive generalization of Kuratowski’s theorem, which defines planarity in terms of two fo
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::28e8649caeb9566e99f4ec2abf4ddb51
https://doi.org/10.1007/978-3-319-66065-3_4
https://doi.org/10.1007/978-3-319-66065-3_4
Publikováno v:
Journal of Knot Theory and Its Ramifications. 27:1850059
A graph is called intrinsically knotted if every embedding of the graph contains a knotted cycle. Johnson, Kidwell and Michael, and, independently, Mattman, showed that intrinsically knotted graphs have at least 21 edges. Recently, Lee, Kim, Lee and
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5c014ed5fdd3ff868037b867d8391c0a
https://doi.org/10.1142/s0218216518500591
https://doi.org/10.1142/s0218216518500591
Publikováno v:
Algebr. Geom. Topol. 9, no. 2 (2009), 743-771
We classify Dehn surgeries on (p,q,r) pretzel knots that result in a manifold of finite fundamental group. The only hyperbolic pretzel knots that admit non-trivial finite surgeries are (-2,3,7) and (-2,3,9). Agol and Lackenby's 6-theorem reduces the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e512a199ce596706c85197722251932e
https://doi.org/10.2140/agt.2009.9.743
https://doi.org/10.2140/agt.2009.9.743