A Polynomial-Time Algorithm for MCS Partial Search Order on Chordal Graphs

We study the partial search order problem (PSOP) proposed recently by Scheffler [WG 2022]. Given a graph $G$ together with a partial order over the vertices of $G$, this problem determines if there is an $\mathcal{S}$-ordering that is consistent with the given partial order, where $\mathcal{S}$ is a graph search paradigm like BFS, DFS, etc. This problem naturally generalizes the end-vertex problem which has received much attention over the past few years. It also generalizes the so-called ${\mathcal{F}}$-tree recognition problem which has just been studied in the literature recently. Our main contribution is a polynomial-time dynamic programming algorithm for the PSOP on chordal graphs with respect to the maximum cardinality search (MCS). This resolves one of the most intriguing open questions left in the work of Sheffler [WG 2022]. To obtain our result, we propose the notion of layer structure and study numerous related structural properties which might be of independent interest.Comment: 12 page

Role of Hydrogen Bonding in Green Fluorescent Protein-like Chromophore Emission.

The fluorescence emission from green fluorescent protein (GFP) is known to be heavily influenced by hydrogen bonding between the core fluorophore and the surrounding side chains or water molecules. Yet how to utilize this feature for modulating the fluorescence of GFP chromophore or GFP-like fluorophore still remains elusive. Here we present theoretical calculations to predict how hydrogen bonding could influence the excited states of the GFP-like fluorophores. These studies provide both a new perspective for understanding the photophysical properties of GFP as well as a solid basis for the rational design of GFP-based fluorophores