Triple-crossing number, the genus of a knot or link and torus knots
Sign Up to like & getrecommendations! Published in 2020 at "Topology and its Applications"
DOI: 10.1016/j.topol.2020.107389
Abstract: Abstract We show that the triple-crossing number of any knot is greater or equal to twice its (canonical) genus and we show an even stronger bound in the case of links. As an application we… read more here.
Keywords: triple crossing; torus knots; genus; crossing number ... See more keywords
ON THE CROSSING NUMBER OF THE CARTESIAN PRODUCT OF A SUNLET GRAPH AND A STAR GRAPH
Sign Up to like & getrecommendations! Published in 2019 at "Bulletin of the Australian Mathematical Society"
DOI: 10.1017/s0004972719000091
Abstract: The exact crossing number is only known for a small number of families of graphs. Many of the families for which crossing numbers have been determined correspond to cartesian products of two graphs. Here, the… read more here.
Keywords: number; product sunlet; crossing number; sunlet graph ... See more keywords
Relative Frequencies of Alternating and Nonalternating Prime Knots and Composite Knots in Random Knot Spaces
Sign Up to like & getrecommendations! Published in 2018 at "Experimental Mathematics"
DOI: 10.1080/10586458.2017.1320239
Abstract: ABSTRACT This article reports the results of an investigation into the average behavior of the knot spectrum (of knots up to 16 crossings) of a family of random knot spaces. A knot space in this… read more here.
Keywords: random knot; knot; crossing number; knot spaces ... See more keywords
A Lower Bound for the Crossing Number of Links in Thickened Surfaces
Sign Up to like & getrecommendations! Published in 2018 at "Siberian Mathematical Journal"
DOI: 10.1134/s0037446618060150
Abstract: We introduce the notion of homological multiplicity for an oriented link in a thickened orientable closed surface. Using the notion, we establish some lower bounds for the crossing number of a link in thickened surfaces. read more here.
Keywords: number links; thickened surfaces; crossing number; bound crossing ... See more keywords
Ribbon 2-knots of ribbon crossing number four
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Knot Theory and Its Ramifications"
DOI: 10.1142/s021821651850058x
Abstract: A [Formula: see text]-knot is a surface in [Formula: see text] that is homeomorphic to [Formula: see text], the standard sphere in [Formula: see text]-space. A ribbon [Formula: see text]-knot is a [Formula: see text]-knot… read more here.
Keywords: see text; formula see; crossing number; ribbon crossing ... See more keywords
The Crossing Number of Join of a Special Disconnected 6-Vertex Graph with Cycle
Sign Up to like & getrecommendations! Published in 2023 at "Mathematics"
DOI: 10.3390/math11102253
Abstract: The crossing number of a graph G, cr(G), is defined as the smallest possible number of edge-crossings in a drawing of G in the plane. There are almost no results concerning crossing number of join… read more here.
Keywords: disconnected vertex; number; vertex graph; crossing number ... See more keywords
Determining Crossing Number of Join of the Discrete Graph with Two Symmetric Graphs of Order Five
Sign Up to like & getrecommendations! Published in 2019 at "Symmetry"
DOI: 10.3390/sym11020123
Abstract: The main aim of the paper is to give the crossing number of the join product G + D n for the disconnected graph G of order five consisting of one isolated vertex and of… read more here.
Keywords: number join; discrete graph; crossing number; order five ... See more keywords