Mathematical Research Seminar - Archive
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A graph is called equimatchable if all of its maximal matchings have the same size. Frendrup et.al. provided a characterization of equimatchable graphs with girth at least 5. In this work, we extend this result by providing a complete structural characterization of equimatchable graphs with girth at least 4, that is, equimatchable graphs with no triangle, by identifying the equimatchable triangle-free graph families. Our characterization also extends the result given by Akbari et. al. which proves that the only connected triangle-free equimatchable r-regular graphs are C5, C7 and Kr,r, where r is a positive integer. Given a non-bipartite graph, our characterization implies a linear time recognition algorithm for triangle-free equimatchable graphs.
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This Monday, October 4, 2021, from 10 am to 11 am.
Everyone is welcome and encouraged to attend.
In this talk I shall speak about Painleve equations, special nonlinear differential equations of second order, that appear in many applications.
I shall explain relation to the recurrence coefficients of certain semiclassical orthogonal polynomials and also show related Hamiltonian systems.
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This Monday, October 11, 2021, from 10 am to 11 am.
Everyone is welcome and encouraged to attend.
We propose a new kind of sliding-block puzzle, called Gourds, where the objective is to rearrange 1 x 2 pieces on a hexagonal grid board of 2n + 1 cells with n pieces, using sliding, turning, and pivoting moves. This puzzle has a single empty cell on a board and forms a natural extension of the 15-puzzle to include rotational moves. We analyze the puzzle and completely characterize the cases when the puzzle can always be solved. We also study the complexity of determining whether a given set of colored pieces can be placed on a colored hexagonal grid board with matching colors. We show this problem is NP-complete for arbitrarily many colors, but solvable in randomized polynomial time if the number of colors is a fixed constant.
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This Monday, October 18, 2021, from 10 am to 11 am.
Everyone is welcome and encouraged to attend.
