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Picavet, Timothe Nguyen, Ngoc-Trung Bui-Xuan, Binh-Minh

Temporal graphs are the modeling of pairwise and historical interaction in recordings of a dataset. A temporal matching formalizes the planning of pair working sessions of a required duration. We depict algorithms finding temporal matchings maximizing the total workload, by an exact algorithm and an approximation. The exact algorithm is a dynamic p...

Diab, A. T. Kaldybekova, B. K. Penkin, O. M.
Published in
Mathematical Notes

Bounds for the multiplicity of the eigenvalues of the Sturm–Liouville problem on a graph, which are valid for a wide class of consistency (transmission) conditions at the vertices of the graph, are given. The multiplicities are estimated using the topological characteristics of the graph. In the framework of the notions that we use, the bounds turn...

Biniaz, Ahmad Bose, Prosenjit Maheshwari, Anil Smid, Michiel

Given a set $P$ of $n$ points in the plane, where $n$ is even, we consider the following question: How many plane perfect matchings can be packed into $P$? For points in general position we prove the lower bound of ⌊log_{2}$n$⌋$-1$. For some special configurations of point sets, we give the exact answer. We also consider some restricted variants of th...

Vladimirov, A. A.
Published in
Mathematical Notes

Aichholzer, Oswin Cabello, Sergio Fabila-Monroy, Ruy Flores-Peñaloza, David Hackl, Thomas Huemer, Clemens Hurtado, Ferran Wood, David R.

A geometric graph is a graph G = (V, E) drawn in the plane, such that V is a point set in general position and E is a set of straight-line segments whose endpoints belong to V. We study the following extremal problem for geometric graphs: How many arbitrary edges can be removed from a complete geometric graph with n vertices such that the remaining...

Chernyshev, V. L. Shafarevich, A. I.
Published in
Mathematical Notes

We study how to construct asymptotic solutions of the spectral problem for the Schrödinger equation on a geometric graph. Differential equations on sets of this type arise in the study of processes in systems that can be represented as a collection of one-dimensional continua interacting only via their endpoints (e.g., vibrations of networks formed...