At the beginning of the series of papers we present systematic approach to exhaust the convex pentagonal tiles of edge-to-edge (EE) tilings. Our procedure is to solve the problem systematically step by step by restricting the candidates to some class. The first task is to classify both of convex pentagons and pentagonal tiling patterns. The classification of the latter is based on the analysis ...

Reported is the new bispidine-derived hexadentate ligand (L = 3-(2-methylpyridyl)-7-(bis-2-methylpyridyl)-3,7-diazabicyclo[3.3.1]nonane) with two tertiary amine and four pyridine donor groups. This ligand can form heterodinuclear and mononuclear complexes and, in the mononuclear compounds discussed here, the ligand may coordinate as a pentadentate ligand, with one of the bispyridinemethane-base...

The paper continues work on monomial ideals in system reliability began by Giglio and Wynn [GW04] following work in discrete tube theory by Naiman and Wynn [NW92, NW97]. The key component is that of multigraded Betti numbers, and an algorithm using MayerVietoris trees by the first author [dC06] is the main tool. First a mapping must be made between the states of a multistate system and a monomi...

We design an approximation algorithm for maximizing \(\alpha\)-bisubmodular function with matroid constraint, where the is a generalization of bisubmodular function. The concept \(\alpha\)- bisubmodularity provided by Huber, Krokhin, and Powell [[1], 2014], rank delta-matroids cut capacity directed networks have \(\alpha\)-bisubmodularity. consider two cases problem, monotone non-monotone objec...

We study max-cut in classes of graphs defined by forbidding a single graph as a subgraph, induced subgraph, or minor. For the first two containment relations, we prove dichotomy theorems. For the minor order, we show how to solve max-cut in polynomial time for the class obtained by forbidding a graph with crossing number at most one (this generalizes a known result for K5-minor-free graphs) and...