Parikshit Chalise

collaborators

4 papers

math.CO2026

All Polyominoes are $C_{4}$ -face-magic

Parikshit Chalise, Richard M. Low, Arman Eisenkolb-Vaithyanathan

For a planar graph $G = (V, E)$ embedded in $R^{2}$ , let $F (G)$ denote the set of faces of $G$ . Then $G$ is called a \textit{ $C_{n}$ -face-magic} graph if there exist…

math.CO2026

Application of the Combinatorial Nullstellensatz to magic-type graph labelings

Parikshit Chalise, Richard M. Low

Let $G = (V, E)$ be a simple graph, and let $k \geq 2$ be an integer. For an edge labeling $h : E (G) \to Z_{k} \ {0}$ , define the induced vertex label by \[ h^+(v)=\su…

math.CO2024

Every tree on $n$ edges decomposes $K_{n x, n x}$ and $K_{2 n x + 1}$

Parikshit Chalise, Antwan Clark, Edinah K. Gnang

We prove that every tree on $n$ edges decomposes $K_{n x, n x}$ and $K_{2 n x + 1}$ for all positive integers $x$ . The said decompositions are obtained by proving that every tree admits…

math.CO2024

A Proof of the Tree Packing Conjecture

Parikshit Chalise, Antwan Clark, Edinah K. Gnang

We prove a conjecture of GyÃ¡rfÃ¡s (1976), which asserts that any family of trees $T_{1}, \dots, T_{n}$ where each $T_{k}$ has $k$ vertices packs into $K_{n}$ . We do so by translating th…

All Polyominoes are C4​-face-magic

Application of the Combinatorial Nullstellensatz to magic-type graph labelings

Every tree on n edges decomposes Knx,nx​ and K2nx+1​

A Proof of the Tree Packing Conjecture

All Polyominoes are $C_{4}$ -face-magic

Every tree on $n$ edges decomposes $K_{n x, n x}$ and $K_{2 n x + 1}$