Puttipong Pongtanapaisan

activity

20152026

most citedOriented Local Moves and Divisibility of the Jones Polynomial

1 citations · 3 across the 20 of their papers we have counts for

collaborators

25 papers

math.CO2026

Ascending, Bridge, and Unknotting Numbers of Knotted Graphs

Bahar Acu, Puttipong Pongtanapaisan, Ritikaa Singhal

In this paper we define the ascending number and bridge number for virtual and welded spatial graphs. We prove that the former admits a lower bound in terms of the latter. This rel…

math.GT2026

Bridge numbers of virtual graphs and handlebody-links

Nikolaos Chantis, Puttipong Pongtanapaisan

We study bridge indices of graphs, virtual graphs, and their handlebody classes. We construct virtual ravels for which the difference between bridge index and weighted overpass bri…

math.GT2026

Bridge position of 3-manifolds embedded in the 5-sphere

Román Aranda, Sarah Blackwell, Geunyoung Kim +2

We introduce and study bridge decompositions for 3-manifolds embedded in the 5-sphere. These generalize both the classical notion of bridge position for knots in the 3-sphere and t…

math.GT2026

Entanglement complexity of spanning pairs of lattice polygons

Ryan Blair, Puttipong Pongtanapaisan, Christine E. Soteros

We study the entanglement complexity of a system consisting of two simple-closed curves (self-avoiding polygons) that span a lattice tube, referred to as a 2SAP. 2SAPs are of inter…

math.GT2025

Trisected Rainbows and Braids

Román Aranda, Scott Carter, Julia Courtney +1

New explicit procedures for passing among triplane diagrams, braid movies, and braid charts for knotted surfaces in $R^{4}$ are presented. To this end, rainbow diagrams, whi…

math.GT2025

Estimating distances in simplicial complexes with applications to 3-manifolds and handlebody-knots

Sayantika Mondal, Puttipong Pongtanapaisan, Hanh Vo

We study distance relations in various simplicial complexes associated with low-dimensional manifolds. In particular, complexes satisfying certain topological conditions with verti…

math.GT2025

Biquandles, quivers and virtual bridge indices

Tirasan Khandhawit, Puttipong Pongtanapaisan, Brandon Wang

We investigate connections between biquandle colorings, quiver enhancements, and several notions of the bridge numbers $b_{i} (K)$ for virtual links, where $i = 1, 2$ . We show that for a…

math.GT2024

Bridge Positions of Links That Cannot Be Monotonically Simplified

Puttipong Pongtanapaisan, Daniel Rodman

For any pair of integers $m$ and $n$ such that $3 < m < n$ , we provide an infinite family of links, where each link in the family has a locally minimal $n$ -bridge position and a global…

math.GT2024

Danceability, A New Definition of Bridge Index

Sol Addison, Sarah Blackwell, Puttipong Pongtanapaisan +3

There are many commonly known definitions of the bridge index coming from combinatorial knot theory, Morse theory, geometry, and algebra. In this paper, we prove that the danceabil…

math.GT2024

Bridge indices of spatial graphs and diagram colorings

Sarah Blackwell, Puttipong Pongtanapaisan, Hanh Vo

We extend the Wirtinger number of links, an invariant originally defined by Blair, Kjuchukova, Velazquez, and Villanueva in terms of extending initial colorings of some strands of…

math.GT2024

Learning bridge numbers of knots

Hanh Vo, Puttipong Pongtanapaisan, Thieu Nguyen

This paper employs various computational techniques to determine the bridge numbers of both classical and virtual knots. For classical knots, there is no ambiguity of what the brid…

math.GT2024

Widths of links via diagram colorings

Ricky Lee, Puttipong Pongtanapaisan, Hanh Vo

In this paper, we define invariants of links in terms of colorings of link diagrams and prove that these invariants coincide with various notions of widths of links with respect to…

math.CO2023

Planar stick indices of some knotted graphs

Tirasan Khandhawit, Puttipong Pongtanapaisan, Athibadee Wasun

Two isomorphic graphs can have inequivalent spatial embeddings in 3-space. In this way, an isomorphism class of graphs contains many spatial graph types. A common way to measure th…

math.QA2023

Quandle coloring quivers and 2-bridge links

Tirasan Khandhawit, Korn Kruaykitanon, Puttipong Pongtanapaisan

The quandle coloring quiver was introduced by Cho and Nelson as a categorification of the quandle coloring number. In some cases, it has been shown that the quiver invariant offers…

math.GT2023

Pants distances of knotted surfaces in 4-manifolds

Román Aranda, Sarah Blackwell, Devashi Gulati +4

We define a pants distance for knotted surfaces in 4-manifolds, which generalizes the complexity studied by Blair-Campisi-Taylor-Tomova for surfaces in the 4-sphere. We determine t…

q-bio.BM2022

Modeling knotted proteins with tangles

Isabel K. Darcy, Garrett Jones, Puttipong Pongtanapaisan

Although rare, an increasing number of proteins have been observed to contain entanglements in their native structures. To gain more insight into the significance of protein knotti…

math.CO2022

Graphoids

Neslihan Gügümcü, Louis H. Kauffman, Puttipong Pongtanapaisan

We study invariants of virtual graphoids, which are virtual spatial graph diagrams with two distinguished degree-one vertices modulo graph Reidemeister moves applied away from the…

math.GT2022

Bounds for Kirby-Thompson invariants of knotted surfaces

Román Aranda, Puttipong Pongtanapaisan, Cindy Zhang

We provide sharp lower bounds for two versions of the Kirby-Thompson invariants for knotted surfaces, one of which was originally defined by Blair, Campisi, Taylor, and Tomova. The…

math.GT2021★ 1 cited

Bounding the Kirby-Thompson invariant of spun knots

Román Aranda, Puttipong Pongtanapaisan, Scott A. Taylor +1

A bridge trisection of a smooth surface in $S^{4}$ is a decomposition analogous to a bridge splitting of a link in $S^{3}$ . The Kirby-Thompson invariant of a bridge trisection measures…

math.GT2021

Bridge numbers and meridional ranks of knotted surfaces and welded knots

Jason Joseph, Puttipong Pongtanapaisan

The Meridional Rank Conjecture asks whether the bridge number of a knot in $S^{3}$ is equal to the minimal number of meridians needed to generate the fundamental group of its complem…

math.GT2020

On keen weakly reducible bridge spheres

Puttipong Pongtanapaisan, Daniel Rodman

A bridge sphere is said to be keen weakly reducible if it admits a unique pair of disjoint compressing disks on opposite sides. In particular, such a bridge sphere is weakly reduci…

math.GT2019

Critical Bridge Spheres for Links with Arbitrarily Many Bridges

Puttipong Pongtanapaisan, Daniel Rodman

We show that for every integer $b \geq 3$ , there exists a link in a $b$ -bridge position with respect to a critical bridge sphere. In fact, for each $b$ , we construct an infinite fam…

math.GT2019★ 1 cited

Oriented Local Moves and Divisibility of the Jones Polynomial

Paul Drube, Puttipong Pongtanapaisan

For any virtual link $L = S \cup T$ that may be decomposed into a pair of oriented $n$ -tangles $S$ and $T$ , an oriented local move of type $T \mapsto T^{'}$ is a replacement of $T$ wi…

math.GT2018

Wirtinger Numbers for Virtual Links

Puttipong Pongtanapaisan

The Wirtinger number of a virtual link is the minimum number of generators of the link group over all meridional presentations in which every relation is an iterated Wirtinger rela…