T. Karthick

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20242026

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4 papers · 1 filter

math.CO2026

Vertex-critical co-gem-free graphs

Manoj Belavadi, T. Karthick

Given a graph $G$ , let $χ (G)$ denote the chromatic number of $G$ . For $k \in N$ , a graph $G$ is $k$ - $v er t e x$ - $cr i t i c a l$ if $χ (G) = k$ and $χ (G - v) < k$ for all $v \in V (G)$ . A r…

math.CO2026

Reconfiguration graph for vertex colorings for ( $P_{2}$ + $P_{3}$ , $C_{4}$ )-free graphs

M. Belavadi, T. Karthick

For a graph $G$ , let $I ¨ (G)$ denote the chromatic number of $G$ . Given a graph $G$ , the $r eco n f i g u r a t i o n$ $g r a p h$ $f or$ $t h e$ $k$ - $co l or in g s$ of $G$ , denoted by $R_{k} (G)$ , is…

math.CO2025

( $P_{2} + P_{4}$ , $K_{4} - e$ )-free graphs are nearly $I ¨ $ -colorable

C. U. Angeliya, T. Karthick, Shenwei Huang

For a graph $G$ , $I ¨ (G)$ and $I ¨ (G)$ respectively denote the chromatic number and clique number of $G$ . In this paper, we show the following results: (i) If $G$ is a ( $P_{2} + P_{4}$ , $K…

math.CO2024

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

Arnab Char, T. Karthick

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

Vertex-critical co-gem-free graphs

Reconfiguration graph for vertex colorings for (P2​+P3​, C4​)-free graphs

(P2​+P4​, K4​−e)-free graphs are nearly I¨-colorable

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

Reconfiguration graph for vertex colorings for ( $P_{2}$ + $P_{3}$ , $C_{4}$ )-free graphs

( $P_{2} + P_{4}$ , $K_{4} - e$ )-free graphs are nearly $I ¨ $ -colorable

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