4 research outputs found

    Linear-Time Recognition of Double-Threshold Graphs

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    A graph G=(V, E) is a double-threshold graph if there exist a vertex-weight function w:V→ℝ and two real numbers lb, ub ∈ ℝ such that uv ∈ E if and only if lb ≤ w(u)+w(v) ≤ ub. In the literature, those graphs are studied also as the pairwise compatibility graphs that have stars as their underlying trees. We give a new characterization of double-threshold graphs that relates them to bipartite permutation graphs. Using the new characterization, we present a linear-time algorithm for recognizing double-threshold graphs. Prior to our work, the fastest known algorithm by Xiao and Nagamochi [Algorithmica 2020] ran in O(n³ m) time, where n and m are the numbers of vertices and edges, respectively

    On the perfect orderability of unions of two graphs

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    A graph G is perfectly orderable if it admits an order < on its vertices such that the sequential coloring algorithm delivers an optimum coloring on each induced subgraph (H, <) of (G, <). A graph is a threshold graph if it contains no P4 , 2K2 or C4 as induced subgraph. A theorem of Chvatal, Hoang, Mahadev and de Werra states that a graph is perfectly orderable if it can be written as the union of two threshold graphs. In this thesis, we investigate possible generalizations of the above theorem. We conjecture that if G is the union of two graphs G1 and G2 then G is perfectly orderable whenever (i) G1 and G2 are both P4 -free and 2K2-free, or (ii) G1 is P4-free, 2K2-free and G2 is P4 -free, C4 -free. We show that the complement of the chordless cycle with at least five vertices cannot be a counter-example to our conjecture and we prove, jointly with Hoang, a special case of (i): if G1 and G2 are two edge disjoint graphs that are P4 -free and 2K2 -free then the union of G1 and G2 is perfectly orderable

    Subject Index Volumes 1–200

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    Fuzzy Sets in Business Management, Finance, and Economics

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    This book collects fifteen papers published in s Special Issue of Mathematics titled “Fuzzy Sets in Business Management, Finance, and Economics”, which was published in 2021. These paper cover a wide range of different tools from Fuzzy Set Theory and applications in many areas of Business Management and other connected fields. Specifically, this book contains applications of such instruments as, among others, Fuzzy Set Qualitative Comparative Analysis, Neuro-Fuzzy Methods, the Forgotten Effects Algorithm, Expertons Theory, Fuzzy Markov Chains, Fuzzy Arithmetic, Decision Making with OWA Operators and Pythagorean Aggregation Operators, Fuzzy Pattern Recognition, and Intuitionistic Fuzzy Sets. The papers in this book tackle a wide variety of problems in areas such as strategic management, sustainable decisions by firms and public organisms, tourism management, accounting and auditing, macroeconomic modelling, the evaluation of public organizations and universities, and actuarial modelling. We hope that this book will be useful not only for business managers, public decision-makers, and researchers in the specific fields of business management, finance, and economics but also in the broader areas of soft mathematics in social sciences. Practitioners will find methods and ideas that could be fruitful in current management issues. Scholars will find novel developments that may inspire further applications in the social sciences
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