J. P. Costalonga

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20122021

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6 papers · 1 filter

math.CO2021

Rooted prism-minors and disjoint cycles containing a specified edge

João Paulo Costalonga, Talmage James Reid, Haindong Wu

Dirac and Lovász independently characterized the $3$ -connected graphs with no pair of vertex-disjoint cycles. Equivalently, they characterized all $3$ -connected graphs with no pris…

math.CO2021

Constructing minimally 3-connected graphs

J. P. Costalonga, R. J. Kingan, S. R. Kingan

A $3$ -connected graph is minimally 3-connected if removal of any edge destroys 3-connectivity. We present an algorithm for constructing minimally 3-connected graphs based on the re…

math.CO2017

A Note on Construction of Dual-Hamiltonian Graphs

João Paulo Costalonga

A connected simple graph is said dual-hamiltonian if its vertex set has a $2$ -coloring such that each color class induces a tree. We call such a coloring a hamiltonian coloring. We…

math.CO2017

Triangle-roundedness in matroids

João Paulo Costalonga, Xianqiang Zhou

A matroid $N$ is said to be triangle-rounded in a class of matroids $M$ if each $3$ -connected matroid $M \in M$ with a triangle $T$ and an $N$ -minor has an $N$ -m…

math.CO2013

On $K_{5}$ and $K_{3, 3}$ -minors of graphs and regular matroids

João Paulo Costalonga

In this paper we prove two main results about obstruction to graph planarity. One is that, if $G$ is a 3-connected graph with a $K_{5}$ -minor and $T$ is a triangle of $G$ , then $G$ h…

math.CO2012

Non-Separating Cocircuits and Graphicness in Matroids

João Paulo Costalonga

Let $M$ be a 3-connected binary matroid and let $Y (M)$ be the set of elements of $M$ avoiding at least $r (M) + 1$ non-separating cocircuits of $M$ . Lemos proved that $M$ is non-graph…

Rooted prism-minors and disjoint cycles containing a specified edge

Constructing minimally 3-connected graphs

A Note on Construction of Dual-Hamiltonian Graphs

Triangle-roundedness in matroids

On K5​ and K3,3​-minors of graphs and regular matroids

Non-Separating Cocircuits and Graphicness in Matroids

On $K_{5}$ and $K_{3, 3}$ -minors of graphs and regular matroids