Anand Babu

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20172026

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6 papers · 1 filter

math.CO2026

Improved bounds for the lazy cops and robbers on generalized hypercubes

Anand Babu, Ashwin Jacob, Karunakaran Murali Krishnan +2

In Lazy Cops and Robbers, at most one cop moves on each cop turn. We study the lazy cop number of the generalized hypercube $Q (n, m)$ , whose vertex set is ${0, 1, \dots, m}^{n}$ . Fo…

math.CO2026

New bounds on the Graham-Pollak theorem for hypergraphs

Anand Babu

For a fixed $r$ , let $f_{r} (n)$ denote the minimum number of complete $r$ -partite $r$ -uniform hypergraphs whose edge sets partition the complete $r$ -uniform hypergraph on $n$ vertice…

math.CO2026

Almost balanced ordered biclique covering of graphs

Anand Babu, Ervin Ranjan, Maddipati Deshith Sai +3

Let $f (n, k)$ be the minimum size of a collection of bicliques such that (i) every edge of the complete graph $K_{n}$ is covered by at least one and at most $k$ bicliques in the colle…

math.CO2026

A counterexample to the conjecture on Biclique Partition number of Split Graphs and related problems

Anand Babu, Ashwin Jacob

The biclique partition number of a graph $G$, denoted $ \operatorname{bp}(G)$, is the minimum number of biclique subgraphs needed to partition the edge set of $G$ . Lyu and Hick…

math.CO2025

Exact Biclique Partition number of Split Graphs

Anand Babu, Ashwin Jacob

The biclique partition number of a graph $G$, denoted $ \operatorname{bp}(G)$, is the minimum number of biclique subgraphs that partition the edge set of $G$. The Graham-Poll…

math.CO2017

Bounds for the Graham-Pollak Theorem for Hypergraphs

Anand Babu, Sundar Vishwanathan

Let $f_{r} (n)$ represent the minimum number of complete $r$ -partite $r$ -graphs required to partition the edge set of the complete $r$ -uniform hypergraph on $n$ vertices. The Graham-P…