Colton Magnant

activity

20102026

most citedTotal rainbow connection of digraphs

23 citations · 67 across the 24 of their papers we have counts for

collaborators

Showing math.COShow all

23 papers · 1 filter

math.CO2026

Monotone Property Thresholds

Colton Magnant, Thor Whalen

This paper was originally written by the authors circa 2005 but was never submitted for publication. The present version corrects minor errors, adds references to work published si…

math.CO2020

Gallai-Ramsey number for the union of stars

Yaping Mao, Zhao Wang, Colton Magnant +1

Given a graph $G$ and a positive integer $k$ , define the \emph{Gallai-Ramsey number} to be the minimum number of vertices $n$ such that any $k$ -edge coloring of the complete graph…

math.CO2020★ 1 cited

Gallai Ramsey number for double stars

Gyula O. H. Katona, Colton Magnant, Yaping Mao +1

Given a graph $G$ and a positive integer $k$ , the \emph{Gallai-Ramsey number} is defined to be the minimum number of vertices $n$ such that any $k$ -edge coloring of $K_{n}$ contains…

math.CO2019

Ramsey and Gallai-Ramsey numbers for stars with extra independent edges

Yaping Mao, Zhao Wang, Colton Magnant +1

Given a graph $G$ and a positive integer $k$ , define the \emph{Gallai-Ramsey number} to be the minimum number of vertices $n$ such that any $k$ -edge coloring of $K_{n}$ contains eith…

math.CO2019★ 2 cited

Properly colored $C_{4}$ 's in edge-colored graphs

Chuandong Xu, Colton Magnant, Shenggui Zhang

When many colors appear in edge-colored graphs, it is only natural to expect rainbow subgraphs to appear. This anti-Ramsey problem has been studied thoroughly and yet there remain…

math.CO2019★ 4 cited

Ramsey and Gallai-Ramsey number for wheels

Yaping Mao, Zhao Wang, Colton Magnant +1

Given a graph $G$ and a positive integer $k$ , define the \emph{Gallai-Ramsey number} to be the minimum number of vertices $n$ such that any $k$ -edge coloring of $K_{n}$ contains eith…

math.CO2019

Note on a generalization of Gallai-Ramsey numbers

Colton Magnant, Zhuojun Magnant

A colored complete graph is said to be Gallai-colored if it contains no rainbow triangle. This property has been shown to be equivalent to the existence of a partition of the verti…

math.CO2019

Gallai-Ramsey number of an 8-cycle

Jonathan Gregory, Colton Magnant, Zhuojun Magnant

Given graphs $G$ and $H$ and a positive integer $k$ , the Gallai-Ramsey number $g r_{k} (G : H)$ is the minimum integer $N$ such that for any integer $n \geq N$ , every $k$ -edge-colori…

math.CO2019★ 5 cited

Gallai-Ramsey numbers for fans

Yaping Mao, Zhao Wang, Colton Magnant +1

Given a graph $G$ and a positive integer $k$ , define the \emph{Gallai-Ramsey number} to be the minimum number of vertices $n$ such that any $k$ -edge coloring of $K_{n}$ contains eith…

math.CO2019

Gallai-Ramsey numbers for rainbow paths

Xihe Li, Pierre Besse, Colton Magnant +2

Given graphs $G$ and $H$ and a positive integer $k$ , the \emph{Gallai-Ramsey number}, denoted by $g r_{k} (G : H)$ is defined to be the minimum integer $n$ such that every coloring o…

math.CO2018★ 5 cited

Ramsey and Gallai-Ramsey numbers for two classes of unicyclic graphs

Zhao Wang, Yaping Mao, Colton Magnant +1

Given a graph $G$ and a positive integer $k$ , define the \emph{Gallai-Ramsey number} to be the minimum number of vertices $n$ such that any $k$ -edge coloring of $K_{n}$ contains eith…

math.CO2018★ 7 cited

Gallai-Ramsey numbers of odd cycles

Zhao Wang, Yaping Mao, Colton Magnant +2

Given two graphs $G$ and $H$ and a positive integer $k$ , the $k$ -color Gallai-Ramsey number, denoted by $g r_{k} (G : H)$ , is the minimum integer $N$ such that for all $n \geq N$ , ev…

math.CO2018

Gallai-Ramsey numbers for books

Jinyu Zou, Yaping Mao, Colton Magnant +2

Given a graph $G$ and a positive integer $k$ , the \emph{Gallai-Ramsey number} is defined to be the minimum number of vertices $n$ such that any $k$ -edge coloring of $K_{n}$ contains…

math.CO2017★ 1 cited

All partitions have small parts - Gallai-Ramsey numbers of bipartite graphs

Haibo Wu, Colton Magnant, Pouria Salehi Nowbandegani +1

Gallai-colorings are edge-colored complete graphs in which there are no rainbow triangles. Within such colored complete graphs, we consider Ramsey-type questions, looking for speci…

math.CO2017

Tight Nordhaus-Gaddum-type upper bound for total-rainbow connection number of graphs

Wenjing Li, Xueliang Li, Colton Magnant +1

A graph is said to be \emph{total-colored} if all the edges and the vertices of the graph are colored. A total-colored graph is \emph{total-rainbow connected} if any two vertices o…

math.CO2017★ 23 cited

Total rainbow connection of digraphs

Hui Lei, Henry Liu, Colton Magnant +1

An edge-coloured path is rainbow if its edges have distinct colours. For a connected graph $G$ , the rainbow connection number (resp. strong rainbow connection number) of $G$ is the…

math.CO2016

Distance proper connection of graphs and their complements

Xueliang Li, Colton Magnant, Meiqin Wei +1

Let $G$ be an edge-colored connected graph. A path $P$ in $G$ is called a distance $ℓ$ -proper path if no two edges of the same color can appear with less than $ℓ$ edges in be…

math.CO2016★ 4 cited

Distance proper connection of graphs

Xueliang Li, Colton Magnant, Meiqin Wei +1

Let $G$ be an edge-colored connected graph. A path $P$ in $G$ is called a distance $ℓ$ -proper path if no two edges of the same color appear with fewer than $ℓ$ edges in betwe…

math.CO2016★ 1 cited

The $(k, ℓ)$ -proper index of graphs

Hong Chang, Xueliang Li, Colton Magnant +1

A tree $T$ in an edge-colored graph is called a {\it proper tree} if no two adjacent edges of $T$ receive the same color. Let $G$ be a connected graph of order $n$ and $k$ be an in…

math.CO2016

Bounds on the connected forcing number of a graph

Randy Davila, Michael Henning, Colton Magnant +1

In this paper, we study (zero) forcing sets which induce connected subgraphs of a graph. The minimum cardinality of such a set is called the connected forcing number of the graph.…

math.CO2016★ 1 cited

On two conjectures about the proper connection number of graphs

Fei Huang, Xueliang Li, Zhongmei Qin +2

A path in an edge-colored graph is called proper if no two consecutive edges of the path receive the same color. For a connected graph $G$ , the proper connection number $p c (G)$ of…

math.CO2016

Solution to a conjecture on the proper connection number of graphs

Fei Huang, Xueliang Li, Zhongmei Qin +1

A path in an edge-colored graph is called a proper path if no two adjacent edges of the path receive the same color. For a connected graph $G$ , the proper connection number $p c (G)$ …

math.CO2014

Enomoto and Ota's conjecture holds for large graphs

Vincent Coll, Alexander Halperin, Colton Magnant +1

In 2000, Enomoto and Ota conjectured that if a graph $G$ satisfies $σ_{2} (G) \geq n + k - 1$ , then for any set of $k$ vertices $v_{1}, \dots, v_{k}$ and for any positive integers $…

Monotone Property Thresholds

Gallai-Ramsey number for the union of stars

Gallai Ramsey number for double stars

Ramsey and Gallai-Ramsey numbers for stars with extra independent edges

Properly colored C4​'s in edge-colored graphs

Ramsey and Gallai-Ramsey number for wheels

Note on a generalization of Gallai-Ramsey numbers

Gallai-Ramsey number of an 8-cycle

Gallai-Ramsey numbers for fans

Gallai-Ramsey numbers for rainbow paths

Ramsey and Gallai-Ramsey numbers for two classes of unicyclic graphs

Gallai-Ramsey numbers of odd cycles

Gallai-Ramsey numbers for books

All partitions have small parts - Gallai-Ramsey numbers of bipartite graphs

Tight Nordhaus-Gaddum-type upper bound for total-rainbow connection number of graphs

Total rainbow connection of digraphs

Distance proper connection of graphs and their complements

Distance proper connection of graphs

The (k,ℓ)-proper index of graphs

Bounds on the connected forcing number of a graph

On two conjectures about the proper connection number of graphs

Solution to a conjecture on the proper connection number of graphs

Enomoto and Ota's conjecture holds for large graphs

Properly colored $C_{4}$ 's in edge-colored graphs

The $(k, ℓ)$ -proper index of graphs