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## König Graphs for 4-Paths: Widened Cycles

P. 45-54.

We characterize the graphs whose induced subgraphs all have the following property: The maximum number of induced 4-paths is equal to the minimum cardinality of the set of vertices such that every induced 4-path contains at least one of them. In this chapter we describe all such graphs obtained from simple cycles by replacing some vertices with cographs.

### In book

Vol. 156. , Switzerland: Springer, 2016

Mokeev D. B., , in: Proceedings of DOOR 2016 Conference, special issue of CEUR Workshop Proceedings. Vol. 1623.: CEUR Workshop Proceedings, 2016.. P. 86-95.

A graph is König for a q-path if every its induced subgraph has the following property. The maximum number of pairwise vertex-disjoint induced paths each on q vertices is equal to the minimum number of vertices, such that removing all the vertices produces a graph having no an induced path on q vertices. In this ...

Added: October 24, 2016

Skiperskih A., Вопросы литературы 2016 № 5 С. 176-190

Human nature’s complexity and contradictoriness, accentuating the enigmatic essence of the Russian mentality, receives a unique depiction in Dostoevsky’s works. Often we read about strange specimens, whose thoughts and actions would bear typical features of Russian culture. The article sets out to examine these features: in particular, duality and a combination of mutually excluding qualities. ...

Added: December 16, 2016

Bykadorov I., Ellero A., Moretti E., , in: Rendiconti per gli Studi Economici quantitativi 2000. .: Venice: Università Ca’Foscari di Venezia, Dipartimento di Matematica Applicata, 2001.. P. 25-39 .

We consider a monopolistic firm that sells seasonal goods. The firm seeks the minimum of the total advertising expenditure during the selling period, given that some previously defined levels of goodwill and sales have to be reached at the end of the period. The only control allowed is on advertising while goodwill and sales levels ...

Added: November 19, 2013

Румынин Д. А., Hristova K., Journal of Algebra 2018 Vol. 515 P. 202-235

We investigate smooth representations of complete Kac-Moody groups. We approach representation theory via geometry, in particular, the group action on the Davis realisation of its Bruhat-Tits building. Our results include an estimate on projective dimension, localisation theorem, unimodularity and homological duality. ...

Added: October 8, 2018

Smirnova N., Tarashnina S., Russian Mathematics 2016 Vol. 60 No. 6 P. 63-74

We understand a solution of a cooperative TU-game as the α-prenucleoli set, α ∈ R, which is a generalization of the notion of the [0, 1]-prenucleolus. We show that the set of all α-nucleoli takes into account the constructive power with the weight α and the blocking power with the weight (1 − α) for all possible values of the parameter α. The ...

Added: July 7, 2016

Feigin B. L., Jimbo M., Mukhin E., Communications in Mathematical Physics 2019 No. 367 P. 455-481

On a Fock space constructed from mn free bosons and lattice Z mn , we give a level n action of the quantum toroidal algebra E m associated to gl m , together with a level m action of the quantum toroidal algebra E n associated to gl n . We prove that the E ...

Added: December 10, 2019

Braginskaya N., Revue des etudes slaves 2016 Vol. 87 No. 1 P. 35-51

The article is devoted to the main theoretical ideas of Russian classicist Olga M. Feidenberg (1890-1955). During her lifetime under a press of Stalinist persecutions and defamation she had published a meager part of her works. And because of association with N.Marr, with whom she collaborated at the early stage of her career, her written ...

Added: October 13, 2017

Matveenko V. D., Montenegrin Journal of Economics 2013 Vol. 9 No. 3 P. 7-27

A new approach is proposed revealing duality relations between a physical side of economy (resources and technologies) and its institutional side (institutional relationsd between social groups). Production function is modeled not as a primal object but rather as a secondary one defined in a dual way by the institutional side. Differential games of bargaining are ...

Added: November 1, 2013

Alekseev V. E., Mokeev D. B., Discrete Applied Mathematics 2016 Vol. 204 P. 1-5

Given a set X, a König graph G for X is a graph with the following property: for every induced subgraph H of G, the maximum number of vertex-disjoint induced subgraphs from X in H is equal to the minimum number of vertices whose deletion from H results in a graph containing no graph in X as an induced subgraph. The purpose of this paper is to characterize all König graphs ...

Added: November 12, 2015

Smirnova N., Тарашнина С. И., Известия высших учебных заведений. Математика 2016 Т. 6 С. 63-74

As a solution concept of cooperative TU-game we propose the set of $\alpha$-prenucleoli, $\alpha\in R$, that is a generalization of the $[0,1]$-prenucleolus. In the paper we show that in a cooperative game the set of $\alpha$-prenucleoli takes into account the constructive power with weight $\alpha$ and the blocking power with weight $(1-\alpha)$ for all possible ...

Added: October 20, 2015

Dietzenbacher B., Estévez-Fernández A., Borm P. et al., Annals of Operations Research 2020

This paper studies bankruptcy problems with nontransferable utility as a generalization of bankruptcy problems with monetary estate and claims. Following the theory on TU-bankruptcy, we introduce a duality notion for NTU-bankruptcy rules and derive several axiomatic characterizations of the proportional rule and the constrained relative equal awards rule. ...

Added: June 2, 2020

Akbarov S. S., Journal of Operator Theory 2022 Vol. 88 No. 1 P. 3-36

In 2013, Yu.N. Kuznetsova constructed a duality theory for Moore groups, based on the idea of a continuous envelope of topological algebra and having the advantage over the existing theories that its enveloping category consists of Hopf algebras in the classical sense. Unfortunately, her work contains several errors, due to which her theory can be considered proved only for ...

Added: August 10, 2022

Zatelepin A., Shchur L., Duality of critical interfaces in Potts model: numerical check / Cornell University. Series "Working papers by Cornell University". 2010. No. 1008.3573.

We report on numerical investigation of fractal properties of critical interfaces in two-dimensional Potts models. Algorithms for finding percolating interfaces of Fortuin-Kasteleyn clusters, their external perimeters and interfaces of spin clusters are presented. Fractal dimensions are measured and compared to exact theoretical predictions. ...

Added: March 7, 2016

Matveenko V. D., , in: Contributions to game theory and management. Issue 6.: St. Petersburg: Graduate School of Management, St. Petersburg University, 2013.. P. 289-300.

In the present paper the game theory is applied to an important open question in economics: providing microfoundations for often-used types of production function. Simple differential games of bargaining are proposed to model a behavior of workers and capital-owners in processes of formation of a set of admissible factor prices or participants’ weights (moral-ethical assessments). ...

Added: November 6, 2013