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Sharp quadratic -binding functions for powers of bipartite graphs
Arpan Sadhukhan, Suraj Kumar Sahoo
For every natural number , we construct powers of bipartite graphs whose chromatic number is quadratic in their clique number, showing that the straightforward qu…
Exact-Distance Domination in Grid Graphs
Sandip Das, Sweta Das, Arpan Sadhukhan
Let be the square grid, and let . A set is an \emph{exact-distance -dominating set} if every vertex has a…
A proof of Seymour's second neighborhood conjecture for oriented graphs with minimum out-degree equal to 7
Arpan Sadhukhan, R. B. Sandeep, Sagnik Sen
We prove Seymour's second neighborhood conjecture on oriented graphs whose minimum out-degree is equal to . This gives, to our knowledge, the first improvement of the minimum ou…
The structure of -free tournaments
Seokbeom Kim, Taite LaGrange, Mathieu Rundström +2
We extend the list of tournaments for which the complete structural description for tournaments excluding as a subtournament is known. Specifically, let be a t…
A Simple Construction of Tournaments with Finite and Uncountable Dichromatic Number
Arpan Sadhukhan
The dichromatic number of a digraph is the minimum number of colors needed to color the vertices in such a way that no monochromatic directed cy…
Shift Graphs, Chromatic Number and Acyclic One-Path Orientations
Arpan Sadhukhan
Shift graphs, which were introduced by Erdős and Hajnal, have been used to answer various questions in extremal graph theory. In this paper, we prove two new results using shift gr…