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math.CO2026
Biregular bipartite labeled multigraphs and perfect matchings in bipartite tensor products
Ilya I. Bogdanov, Fedor Petrov, Anton Sadovnichiy +1
In 2019, P. Higgins formulated [1] a question about bipartite graphs (see Conjecture 1 below); this question arises in the study of regular finite semigroups. F. V. Petrov formulat…
math.CO2025
On forest and bipartite cuts in sparse graphs
Ilya I. Bogdanov, Elizaveta Neustroeva, Georgy Sokolov +3
The paper is devoted to sufficient conditions for the existence of vertex cuts in simple graphs, where the induced subgraph on the cut vertices belongs to a specified graph class.…
math.CO2022
The continualization approach to the on-line hypergraph coloring
Margarita Akhmejanova, Ilya Bogdanov, Grigory Chelnokov
The paper deals with an algorithmic problem concerning combinatorial game theory. Here we introduce and analyze a continuous generalization of Chip Game from the work of Duraj, Gut…