Boram Park

activity

20242026

collaborators

8 papers

math.CO2026

Connectivity keeping paths in digraphs

Hojin Chu, Boram Park, Homoon Ryu

Mader conjectured that every $k$ -strong digraph $D$ with minimum semidegree $δ^{0} (D) \geq 2 k + m - 1$ contains a dipath $P$ of order $m$ such that $D - V (P)$ remains $k$ -strong. For $k = 1$ ,…

math.CO2026

Minimum degree conditions for removable matchings in $k$ -connected graphs

Hojin Chu, Ringi Kim, Boram Park

In 1969, Halin proved that every $k$ -connected graph $G$ with minimum degree at least $k + 1$ contains an edge $e$ such that $G - e$ is $k$ -connected. As an edge is a matching of size…

math.CO2025

Connectivity keeping trees in triangle-free graphs

Hojin Chu, Shinya Fujita, Boram Park +1

In 2012, Mader conjectured that for any tree $T$ of order $m$ , every $k$ -connected graph $G$ with minimum degree at least $⌊ \frac{3 k}{2} ⌋ + m - 1$ contains a subtree $T'\c…

math.CO2025

On Alon-Tarsi orientations of sparse graphs

Eun-Kyung Cho, Ilkyoo Choi, Boram Park +1

Assume $G$ is a graph, $(v_{1}, \dots, v_{k})$ is a sequence of distinct vertices of $G$ , and $(a_{1}, \dots, a_{k})$ is an integer sequence with $a_{i} \in {1, 2}$ . We say $G$ is \emph{$(a_1…

math.CO2025

On $2$ -connected graphs avoiding cycles of length $0$ modulo $4$

Hojin Chu, Boram Park, Homoon Ryu

For two integers $k$ and $ℓ$ , an $(ℓ mod k)$ -cycle means a cycle of length $m$ such that $m \equiv ℓ (mod k)$ . In 1977, Bollobás proved a conjecture of Burr and Erd…

math.CO2025

Obstructions for homomorphisms to odd cycles in series-parallel graphs

Eun-Kyung Cho, Ilkyoo Choi, Boram Park +1

For a graph $H$ , an $H$ -colouring of a graph $G$ is a vertex map $ϕ : V (G) \to V (H)$ such that adjacent vertices are mapped to adjacent vertices. A graph $G$ is $C_{2 k + 1}$ -critical i…

math.CO2025

Tight upper bounds on the hop domination number of triangle-free graphs

Shinya Fujita, Boram Park

For a graph $G$ , a subset $S$ of $V (G)$ is a {\it hop dominating set} of $G$ if every vertex not in $S$ has a $2$ -step neighbor in $S$ . The {\it hop domination number}, $γ_{h} (G)$ , o…

math.CO2024

Monochromatic $k$ -connection of graphs

Qingqiong Cai, Shinya Fujita, Henry Liu +1

An edge-coloured path is monochromatic if all of its edges have the same colour. For a $k$ -connected graph $G$ , the monochromatic $k$ -connection number of $G$ , denoted by $m c_{k} (G)$ …

Connectivity keeping paths in digraphs

Minimum degree conditions for removable matchings in k-connected graphs

Connectivity keeping trees in triangle-free graphs

On Alon-Tarsi orientations of sparse graphs

On 2-connected graphs avoiding cycles of length 0 modulo 4

Obstructions for homomorphisms to odd cycles in series-parallel graphs

Tight upper bounds on the hop domination number of triangle-free graphs

Monochromatic k-connection of graphs

Minimum degree conditions for removable matchings in $k$ -connected graphs

On $2$ -connected graphs avoiding cycles of length $0$ modulo $4$

Monochromatic $k$ -connection of graphs