T. Murthy

activity

20172021

most citedProblems on Matchings and Independent Sets of a Graph

9 citations · 13 across the 4 of their papers we have counts for

collaborators

4 papers

math.GM2021

Hadwiger number always upper bounds the chromatic number -- 1852-1943 -- A far-reaching generalisation of Guthrie's postulate

T Srinivasa Murthy

In a simple graph $G$ , we prove that the \textit{Hadwiger number}, $h (G)$ , of the given graph $G$ always upper bounds the \textit{chromatic number}, $χ (G)$ , of the given graph $G$ ,…

math.CO2020★ 4 cited

A proof of the Total Coloring Conjecture

T Srinivasa Murthy

\textit{Total Coloring} of a graph is a major coloring problem in combinatorial mathematics, introduced in the early $1960$ s. A \textit{total coloring} of a graph $G$ is a map $f:V…

math.CO2019

Connected-Intersecting Families of Graphs

Aaron Berger, Ross Berkowitz, Pat Devlin +4

For a graph property $P$ and a common vertex set $V = {1, 2, \dots, n}$ , a family of graphs on $V$ is \emph{ $P$ -intersecting} iff $G \cap H$ satisfies $\math…

math.CO2017★ 9 cited

Problems on Matchings and Independent Sets of a Graph

Amitava Bhattacharya, Anupam Mondal, T. Srinivasa Murthy

Let $G$ be a finite simple graph. For $X \subset V (G)$ , the difference of $X$ , $d (X) := ∣ X ∣ - ∣ N (X) ∣$ where $N (X)$ is the neighborhood of $X$ and $max {d (X) : X \subset V (G)}$ …