Kombinatorikus Optimalizálás: Algoritmusok, Strukturák, Alkalmazások = Combinatorial optimization: algorithms, structures, applications

Mint azt az OTKA-pályázat munkaterve tartalmazza, a pályázatban résztvevő kutatók alkotják a témavezető irányításával működő Egerváry Jenő Kombinatorikus Optimalizálási Kutatócsoportot. A csoport a kutatási tervben szereplő több témában jelentős eredményeket ért el az elmúlt 4 évben, ezekről a pályázat résztvevőinek több mint 50 folyóiratcikke jelent meg, és számos rangos nemzetközi konferencián ismertetésre kerültek. Néhány kiemelendő eredmény: sikerült polinomiális kombinatorikus algoritmust adni irányított gráf pont-összefüggőségének növelésére; jelentős előrelépés történt a háromdimenziós térben merev gráfok jellemzésével és a molekuláris sejtéssel kapcsolatban; 2 dimenzióban sikerült bizonyítani Hendrickson sejtését; a párosításelméletben egy újdonságnak számító módszerrel számos új algoritmikus eredmény született; több, gráfok élösszefüggőségét jellemző tételt sikerült hipergráfokra általánosítani. | As the research plan indicates, the researchers participating in the project are the members of the Egerváry Research Group, led by the coordinator. The group has made important progress in the past 4 years in the research topics declared in the research plan. The results have been published in more than 50 journal papers, and have been presented at several prestigious international conferences. The most significant results are the following: a polynomial algorithm has been found for the node-connectivity augmentation problem of directed graphs; considerable progress has been made towards the characterization of 3-dimensional rigid graphs and towards the proof of the molecular conjecture; Hendrickson's conjecture has been proved in 2 dimensions; several new algorithmic results were obtained in matching theory using a novel approach; several theorems characterizing connectivity properties of graphs have been generalized to hypergraphs

On the uniqueness of the Laplacian spectra of coalescence of complete graphs

Acknowledgments: I would like to thank Nicole Snashall for her encouragement, comments and support. I also would like to thank Jozef Siran for his comments on amalgamations, which led to more thinking about defining my graphs. This project started with an application to social networks; however, it developed into a much more general study. I would like to dedicate this paper to the memory of Alto Zeitler (1945-2022), my mathematics teacher.Peer reviewedPublisher PD

A detachment algorithm for inferring a graph from path frequency

Abstract: Inferring graphs from path frequency has been studied as an important problem which has a potential application to drug design and elucidation of chemical structures. Given a multiple set g of strings of labels with length at most K, the problem asks to find a vertex-labeled graph G that attains a one-to-one correspondence between g and the occurrences of labels along all paths of length at most K in G. In this paper, we prove that the problem with K = 1 can be formulated as a problem of finding a loopless and connected detachment, based on which an efficient algorithm for solving the problem is derived. Our algorithm also solves the problem with an additional constraint such that every vertex in an inferred graph is required to have a specified degree