The List Coloring Reconfiguration Problem for Bounded Pathwidth Graphs

We study the problem of transforming one list (vertex) coloring of a graph into another list coloring by changing only one vertex color assignment at a time, while at all times maintaining a list coloring, given a list of allowed colors for each vertex. This problem is known to be PSPACE-complete for bipartite planar graphs. In this paper, we first show that the problem remains PSPACE-complete even for bipartite series-parallel graphs, which form a proper subclass of bipartite planar graphs. We note that our reduction indeed shows the PSPACE-completeness for graphs with pathwidth two, and it can be extended for threshold graphs. In contrast, we give a polynomial-time algorithm to solve the problem for graphs with pathwidth one. Thus, this paper gives precise analyses of the problem with respect to pathwidth

Reconfiguration of Colorable Sets in Classes of Perfect Graphs

A set of vertices in a graph is c-colorable if the subgraph induced by the set has a proper c-coloring. In this paper, we study the problem of finding a step-by-step transformation (reconfiguration) between two c-colorable sets in the same graph. This problem generalizes the well-studied Independent Set Reconfiguration problem. As the first step toward a systematic understanding of the complexity of this general problem, we study the problem on classes of perfect graphs. We first focus on interval graphs and give a combinatorial characterization of the distance between two c-colorable sets. This gives a linear-time algorithm for finding an actual shortest reconfiguration sequence for interval graphs. Since interval graphs are exactly the graphs that are simultaneously chordal and co-comparability, we then complement the positive result by showing that even deciding reachability is PSPACE-complete for chordal graphs and for co-comparability graphs. The hardness for chordal graphs holds even for split graphs. We also consider the case where c is a fixed constant and show that in such a case the reachability problem is polynomial-time solvable for split graphs but still PSPACE-complete for co-comparability graphs. The complexity of this case for chordal graphs remains unsettled. As by-products, our positive results give the first polynomial-time solvable cases (split graphs and interval graphs) for Feedback Vertex Set Reconfiguration

Quantitative evaluation of thermodynamic parameters for thermal back-reaction after mechanically induced fluorescence change

Kinetics of the thermal back-reaction of beta-diketonate boron difluoride complexes after mechanical perturbation were evaluated by fluorescence intensity changes for the first time, suggesting that the activation parameters of the reaction intermediates governed intermolecular interactions such as hydrogen bonding assisted by substituent groups.ArticleRSC ADVANCES. 3(43):19785-19788 (2013)journal articl

Shortest Reconfiguration of Perfect Matchings via Alternating Cycles

Motivated by adjacency in perfect matching polytopes, we study the shortest reconfiguration problem of perfect matchings via alternating cycles. Namely, we want to find a shortest sequence of perfect matchings which transforms one given perfect matching to another given perfect matching such that the symmetric difference of each pair of consecutive perfect matchings is a single cycle. The problem is equivalent to the combinatorial shortest path problem in perfect matching polytopes. We prove that the problem is NP-hard even when a given graph is planar or bipartite, but it can be solved in polynomial time when the graph is outerplanar

Complexity of the Multi-Service Center Problem

The multi-service center problem is a variant of facility location problems. In the problem, we consider locating p facilities on a graph, each of which provides distinct service required by all vertices. Each vertex incurs the cost determined by the sum of the weighted distances to the p facilities. The aim of the problem is to minimize the maximum cost among all vertices. This problem is known to be NP-hard for general graphs, while it is solvable in polynomial time when p is a fixed constant. In this paper, we give sharp analyses for the complexity of the problem from the viewpoint of graph classes and weights on vertices. We first propose a polynomial-time algorithm for trees when p is a part of input. In contrast, we prove that the problem becomes strongly NP-hard even for cycles. We also show that when vertices are allowed to have negative weights, the problem becomes NP-hard for paths of only three vertices and strongly NP-hard for stars

Fluorescence properties of nanoaggregates of pyrene ammonium derivative and its photoinduced dissolution and reaction in tetrahydrofuran/aqueous solutions

We studied the fluorescence properties of nanoaggregates of pyrene ammonium derivative (PyAm) and their photoinduced dissolution and reaction in tetrahydrofuran (THF)/aqueous solution. The final concentration (dye concentration after reprecipitation) dependence of the fluorescence peak was measured. The fluorescence peak of PyAm that originated from the excimer is shifted to the long wavelength side increasing with the final concentration, which is ascribable to the characteristic fluorescence spectral changes depending on their size. The size-dependent fluorescence change in the nanoaggregates is related to some molecular conformation, packing, and elastic properties of the nanoparticles at the surface. To understand the fluorescence properties of the intermediates from aggregates to crystals is important for the studies of organic nanocrystals/aggregates prepared by the reprecipitation methods. We also determined the fluorescence spectra of the PyAm nanoaggregates in a THF/aqueous solution by photoinduced dissolution and reaction. It originated from the photochemical reaction between PyAm and THF. Changes in the perpendicular light scattering intensity by photoirradiation supports the photoinduced dissolution of PyAm in the THF/aqueous solution. These findings are important in the research field of photochemical reactions in organic nanocrystals.ArticleRESEARCH ON CHEMICAL INTERMEDIATES. 41(9):6897-6906 (2015)journal articl