Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, August 25, 2015.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
      July 2015             August 2015           September 2015
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2  3  4                      1          1  2  3  4  5
5  6  7  8  9 10 11    2  3  4  5  6  7  8    6  7  8  9 10 11 12
12 13 14 15 16 17 18    9 10 11 12 13 14 15   13 14 15 16 17 18 19
19 20 21 22 23 24 25   16 17 18 19 20 21 22   20 21 22 23 24 25 26
26 27 28 29 30 31      23 24 25 26 27 28 29   27 28 29 30
30 31


Tuesday, August 25, 2015

1:00 pm in 241 Altgeld Hall,Tuesday, August 25, 2015

#### Informal get together

Abstract: Stefan Bergman once said "No derivatives, no lunch". We will briefly meet and introduce two new postdocs; those who haven't had lunch might decide to do so. First official meeting will be Sept. 1.

3:00 pm in 241 Altgeld Hall,Tuesday, August 25, 2015

#### Favaron's Theorem, k-dependence, and Tuza's Conjecture

###### Gregory J. Puleo   [email] (Coordinated Science Lab UIUC)

Abstract: A vertex set D in a graph G is k-dependent if G[D] has maximum degree at most k-1, and k-dominating if every vertex outside D has at least k neighbors in D. Favaron proved that if D is a k-dependent set maximizing the quantity k|D| - |E(G[D])|, then D is k-dominating. We extend this result, showing that such sets satisfy a stronger structural property, and we find a surprising connection between Favaron's theorem and a conjecture of Tuza regarding packing and covering of triangles.

3:00 pm in 243 Altgeld Hall,Tuesday, August 25, 2015