Arnab Char

activity

20162025

most citedSpectra of general hypergraphs

94 citations · 106 across the 9 of their papers we have counts for

collaborators

9 papers

math.CO2025

Edge-colouring and orientations: applications to degree- and $χ$ -boundedness

Arnab Char, Ken-ichi Kawarabayashi, Lucas Picasarri-Arrieta

We prove a new generalisation of Ramsey's theorem by showing that every $2$ -edge-coloured graph with sufficiently large minimum degree contains a monochromatic induced subgraph who…

cs.DM2025

$4 K_{1}$ -free graph with the cop number $3$

Arnab Char, Paras Vinubhai Maniya, Dinabandhu Pradhan

The game of cops and robber is a two-player turn-based game played on a graph where the cops try to capture the robber. The cop number of a graph $G$ , denoted by $c (G)$ is the mini…

cs.DM2025

On near optimal colorable graphs

C. U. Angeliya, Arnab Char, T. Karthick

A class of graphs $G$ is said to be \emph{near optimal colorable} if there exists a constant $c \in N$ such that every graph $G \in G$ satisfies $χ(G) \leq \max\{c…

math.CO2024

An optimal chromatic bound for ( $P_{2} + P_{3}$ , gem)-free graphs

Arnab Char, T. Karthick

Given a graph $G$ , the parameters $χ (G)$ and $ω (G)$ respectively denote the chromatic number and the clique number of $G$ . A function $f : N \to N$ such t…

math.CO2023★ 2 cited

On graphs with no induced $P_{5}$ or $K_{5} - e$

Arnab Char, T. Karthick

In this paper, we are interested in some problems related to chromatic number and clique number for the class of $(P_{5}, K_{5} - e)$ -free graphs, and prove the following. $(a)$ If $G$ is…

math.CO2022

Optimal chromatic bound for ( $P_{2} + P_{3}$ , $P_{2} + P_{3} ˉ$ )-free graphs

Arnab Char, T. Karthick

For a graph $G$ , let $χ (G)$ ( $ω (G)$ ) denote its chromatic (clique) number. A $P_{2} + P_{3}$ is the graph obtained by taking the disjoint union of a two-vertex path $P_{2}$ and a three-ver…

math.CO2020★ 8 cited

Coloring of ( $P_{5}$ , $4$ -wheel)-free graphs

Arnab Char, T. Karthick

For a graph $G$ , $χ (G)$ $(ω (G))$ denote its chromatic (clique) number. A $P_{5}$ is the chordless path on five vertices, and a $4$ - $w h ee l$ is the graph consisting of a chordless cycl…

math.SP2017★ 2 cited

On the spectrum of directed uniform and non-uniform hypergraphs

Anirban Banerjee, Arnab Char

Here, we suggest a method to represent general directed uniform and non-uniform hypergraphs by different connectivity tensors. We show many results on spectral properties of undire…

math.SP2016★ 94 cited

Spectra of general hypergraphs

Anirban Banerjee, Arnab Char, Bibhash Mondal

Here, we show a method to reconstruct connectivity hypermatrices of a general hypergraph (without any self loop or multiple edge) using tensor. We also study the different spectral…

Edge-colouring and orientations: applications to degree- and χ-boundedness

4K1​-free graph with the cop number 3

On near optimal colorable graphs

An optimal chromatic bound for (P2​+P3​, gem)-free graphs

On graphs with no induced P5​ or K5​−e

Optimal chromatic bound for (P2​+P3​, P2​+P3​ˉ​)-free graphs

Coloring of (P5​, 4-wheel)-free graphs

On the spectrum of directed uniform and non-uniform hypergraphs

Spectra of general hypergraphs

Edge-colouring and orientations: applications to degree- and $χ$ -boundedness

$4 K_{1}$ -free graph with the cop number $3$

An optimal chromatic bound for ( $P_{2} + P_{3}$ , gem)-free graphs

On graphs with no induced $P_{5}$ or $K_{5} - e$

Optimal chromatic bound for ( $P_{2} + P_{3}$ , $P_{2} + P_{3} ˉ$ )-free graphs

Coloring of ( $P_{5}$ , $4$ -wheel)-free graphs