**2014 - 2015**

**Tuesday, March 31**

**Speaker: Jennifer Aust**

Title: Bounded Complete Embedding Graphs

**Thursday, April 2**

**Speaker: Liz McInnis**

Title: Tilings of graphs

**Thursday, April 16**

**Speaker: Alex Rosa**, McMaster University

Title: TBA

**Tuesday, April 21**

**Speaker: Mariusz Meszka**, AGH University of Science and Technology, Krakow, Poland

Title: TBA

**Thursday, March 12**

**Speaker: A J W Hilton**, University of Reading and Queen Mary College University of London, UK

Abstract: We generalize Hall's Condition for a system of distinct representatives and apply it to obtain results about completing latin squares. A latinized square is a generalization of a latin square. We have a set v1,v2,.....,vn of positive integers and a positive integer p such that v1 + v2 + .......+vn = p^2 and 1 <= vi <=p. A p x p array on symbols x1, x2, ......,xn such that each xi occurs vi times, and no xi occurs twice in any row or column is a (v1,v2,......,vn)-latinized square. We give some completion results for this type of square.

**Thursday, March 19**

**Speaker: James Hammer**

Title: TBA

**Thursday, February 26**

**Speaker: Pete Johnson**

Title: Minimum (n,k,t) graphs

Abstract: Suppose that n, k, and t are positive integers, in non-increasing order. An (n,k,t) graph is a simple graph on n vertices such that every induced subgraph on k vertices has a complete subgraph on t vertices. A minimum (n,t,k)graph is an (n,k,t)graph with the minimum number of edges possible for such a graph. The case t = 2 is intriguing because the unique minimum (n,k,2) graph is the complemenet of the Turan graph on n vertices with k - 1 parts, by Turan's theorem.

Our (Dean Hoffman's, Jessica McDonald's, and my) conjecture is that for every n, k,and t, there is a minimum (n,k,t) graph whose every component is a clique--call it a cligue graph, for short. This talk will show how to obtain, for each n, k, and t, all graphs with the minimum number of edges among (n,k,t) graphs which are clique graphs.

**Tuesday, February 24**

**Speaker: ABBALABBA**

Title: Fractional isomorphisms of Cayley graphs

**Tuesday**, **February 17**

**Speaker:** **Dean Hoffman**

Topic: A nice NP_Complete argument for a digraph problem

**Tuesday, February 10**

**Speaker: Vitaly Voloshin**,Troy University

Topic: Hypertrees and cycles in hypergraphs

Abstract: A hypertree is a hypergraph isomorphic to a family of sub trees of a tree. In hypergraphs, hypertrees play a role similar to the role of trees in graphs with the only distinction: it is MUCH MORE interesting! We will discuss some properties of hypertrees and their relation to other remarkable classes of hypergraphs.

**Thursday, February 5**

Topic: CCL, An open problem on 5-cycle systems

**Thursday, January 22**

**Speaker: Pete Johnson**

Title: Some problems concerning the secure-domination numbers of graphs

**Tuesday, January 20**

**Speaker: Dean Hoffman**

Topic: A puzzle I can't seem to solve!

**Tuesday, December 2**

Combinatorics faculty meeting.....courses for next year. Be there or be square!

**Thursday,** **November 20**

**Speaker: Suil O**, Georgia State University

Title: Edge-connectivity in regular multigraphs from eigenvalues

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**Tuesday, November 4**

**Speaker: Amin Bahmanian**

Title: Extending factorizations of complete uniform hypergraphs

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**Thursday, October 30**

**Speaker: Vitaly Voloshin, Troy University
** Topic: Some open problems in hypergraph coloring

**Tuesday, October 21**

**Speaker: Jessica McDonald**

Title: A list analog of Vizing's Theorem for simple graphs with triangles but no other odd cycles

**Tuesday, October 14**

**Speaker: Curt Lindner**

Topic: How to embed a partial odd cycle system

**Thursday, October 9**

**NO SEMINAR**

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**Tuesday, September 30**

**Speaker: Pete Johnson**

Topic: Later developments concerning Hall's Condition and list coloring

**Thursday, September 25**

**NO SEMINAR**

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**Tuesday, September 23**

**Speaker: Pete Johnson**

**Topic: Another chapter in the history of list-coloring**

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**Thursday, September 18**

**Topic:** CCL, Graph theory and universal algebra go hand in hand!

**Tuesday, September 16**

**NO SEMINAR**

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**Thursday, September 11**

**Speaker: Doug Leonard**

Topic: Coordinates other than affine or projective

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**Tuesday, September 9**

**Speaker: Pete Johnson**

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**Thursday, September 4**

**Speaker: Dean Hoffman**, continued

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**Tuesday, September 2**

**NO SEMINAR**

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**Thursday, August 28**

**Speaker: Saad El-Sanati, Illinois State University**

**Title:** On decomposing regular graphs and multigraphs into isomorphic trees and fore**sts**

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**Tuesday, August 26**

**Speaker: Dean Hoffman
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**Thursday, August 21**

** Title: **CCL, How to squash a 6-cycle system into a Steiner triple system

**Tuesday, August 19**

**ORGANIZATIONAL MEETING**