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Seminars in Combinatorics and Optimization
Algebraic Graph Theory - Dmitriy Panasenko
Title: Deza graphs and vertex connectivity
| Speaker: | Dmitriy Panasenko |
| Affiliation: | Umeå University |
| Location: | Please contact Sabrina Lato for Zoom link. |
Abstract: A k-regular graph on v vertices is called a Deza graph with parameters (v, k, b, a), b ≥ a if the number of common neighbors of any two distinct vertices takes two values: a or b. A Deza graph is called a strictly Deza graph if it has diameter 2 and is not strongly regular.
In this talk we will discuss the enumeration of strictly Deza graphs and the enumeration of special subclass of strictly Deza graphs called divisible design graphs. We will also describe the constructions of divisible design graphs found during the enumeration.
C&O Special Seminar - Vijay Vazirani
Title: A Theory of Alternating Paths and Blossoms, from the Perspective of Minimum Length - Part 1
| Speaker: | Vijay Vazirani |
| Affiliation: | University of California, Irvine |
| Location: | MC 5479 |
Abstract: It is well known that the proof of some prominent results in mathematics took a very long time --- decades and even centuries. The first proof of the Micali-Vazirani (MV) algorithm, for finding a maximum cardinality matching in general graphs, was recently completed --- over four decades after the publication of the algorithm (1980). MV is still the most efficient known algorithm for the problem. In contrast, spectacular progress in the field of combinatorial optimization has led to improved running times for most other fundamental problems in the last three decades, including bipartite matching and max-flow.
The new ideas contained in the MV algorithm and its proof remain largely unknown, and hence unexplored, for use elsewhere.
The purpose of this two-talk-sequence is to rectify that shortcoming.
C&O Special Seminar - Vijay Vazirani
Title: A Theory of Alternating Paths and Blossoms, from the Perspective of Minimum Length - Part 2
| Speaker: | Vijay Vazirani |
| Affiliation: | University of California, Irvine |
| Location: | MC 5479 |
Abstract: It is well known that the proof of some prominent results in mathematics took a very long time --- decades and even centuries. The first proof of the Micali-Vazirani (MV) algorithm, for finding a maximum cardinality matching in general graphs, was recently completed --- over four decades after the publication of the algorithm (1980). MV is still the most efficient known algorithm for the problem. In contrast, spectacular progress in the field of combinatorial optimization has led to improved running times for most other fundamental problems in the last three decades, including bipartite matching and max-flow.
The new ideas contained in the MV algorithm and its proof remain largely unknown, and hence unexplored, for use elsewhere.
The purpose of this two-talk-sequence is to rectify that shortcoming.