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Talks:
Place: The Seminar Room of Department of Mathematics 304/1,
Shahid Beheshti University
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Seminars, Workshops , Conferences:
Weekly Seminar of SBU
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Title:
Generalized Fisher inequality
Speaker:
Dr Elaheh Khamseh
Time and Date: 10:00-11:30, Saturday, 26 November, 2011
زمان:
شنبه 5 آذر 1390
ساعت 11:30-10:00
Abstract:
In this talk, we present miniatures 3 and 4 of the book thirty three
miniatures. In fact, we present the proof of following theorems:
Theorem 1. If we have n citizens and m clubs such that each club has
to have an odd number of members and every two clubs must have an even
number of members in common, then m≤n.
Theorem 2. If C_1,...,C_m are distinct and nonempty subsets of an
n-element set such that all the intersections C_i ∩ C_j have the
same size, them m≤n.
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Title:
Hypercubes: Problems and
applications
Speaker: Professor Ebadollah S.
Mahmoodian
Time and Date:
10:30-12:00,
Saturday, 19 November, 2011
زمان:
شنبه 28 آبان 1390
ساعت 12:00-10:30
Abstract: Hypercubes
are very interesting objects which arise in many different
areas of mathematics. As a graph, a hypergraph Q_n is
a graph in which the
vertices are all binary vectors of length n, and two vertices are adjacent
if
and only if the Hamming distance between them is 1, i.e. their components
differ in one place. Hypercubes have many applications and there are many
challenging conjectures about them. In this talk we discuss some of these
conjectures and the applications. Our emphasis will be on square coloring,
galactic number and forced matchings.
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Title:
Graph Minors
Theory
Speaker: Bahman Ghandchi
Time and Date: 10:00-11:30, Saturday, 5
November, 2011
زمان:
شنبه 14 آبان 1390
ساعت 11:30-10:00
Abstract: For a given graph $G$ we say graph $H$ is a minor of $G$ if it
can be obtained from $G$ by a sequence of vertex deletions, edge deletions
and edge contractions. Many Graph theorists admit that the most important
unsolved problem in Graph theory is a conjecture by Hadwiger which states
for every graph $G$ the graph $k_{\chi(G)}$ is a minor of $G$. This
conjecture has led to a great interest among graph theorist and
combinatorists to study Graph Minors Theory.
In this short talk we will cover
basic definitions of Graph Minors Theory along with some interesting
results in the field including but not limited to:
1- Hadwiger's conjecture
2- Extremal problems in Graph Minors Theory
3- Well quasi ordering and Wagner's conjecture
4- Graph Minors project by Seymour and Robertson
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Title: Fractional Covering and Packing
Speaker: Farokhlagha Moazami
Time and Date: 10:00-11:30,
Saturday, 29 October, 2011
زمان: شنبه 7
آبان 1390 ساعت 11:30-10:00
Abstract: Our purpose in this talk is to reveal the rational side of
graph theory. We seek to convert integer-based definitions and invariants
into their fractional analogues. When we do this, we want to be sure that
we have formulated the "right" definitions— conversions from
integer to real that are, in some sense, natural. Here are two ways
we might judge if an integer-to-real conversion process is natural: First, when
two seemingly disparate conversions yield the same concept, then we feel
confident that the fractionalized concept is important (and not tied to how
we made the conversion). Second, when the same conversion process works for
a variety of concepts, then we feel we have arrived at a reasonable way to
do the integer-to-real transformation. If a variety of attractive theorems
arise from the new definition, then we can be certain that we are on the
right track.
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Title:
Again Erdos's High
Girth-High Chromatic Number Theorem
Speaker: Saeed Shaebani
Time and Date: 10:00-11:30, Saturday, 8 October, 2011
زمان:
شنبه 16 مهر 1390
ساعت 11:30-10:00
Abstract: Erdos's celebrated theorem on
High Girth-High Chromatic Number, states that for each naturak number k,
there exists a graph G that min{χ(G) , g(G)} > k ,
where χ(G) and g(G) stand for the chromatic number of G and
the girth of G, respectively. This theorem maybe the beginning of using
Probabilistic Methods in Combinatorics. In this talk, first we describe a
new simple and nice proof of this theorem that uses only counting
arguments. Then we talk about famous Shift Graphs that
provide graphs with High Odd-Girth and High Chromatic
Number. Finally, we decribe an application of Shift Graphs in a short
proof of Welzl's Homomorphism Density Theorem.
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Title: A sharp bound for the number of sets that pairwise intersect at k positive values
Speaker: Farokhlagha Moazami
Time and Date: 10:00-11:30, Saturday, 1 October, 2011
Abstract: In this talk we
prove that if L is a set of k positive integers and
{A1,. . .,Am} is a family of subsets of an n-element set
satisfying |Ai ∩Aj| belongs
to L, for all 1 ≤ i < j ≤m,
then m≤ \sum_{i=0}^k {n-1 \choose i}. The case k=1 was proven
50 years ago by Majumdar.
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Title: On conflict-free
coloring
Speaker: Erfan Rostami
Time and Date:
12:45-14:00, Sunday, 10 July, 2011
Abstract: A conflict-free
coloring of a hypergraph H = (V,E) is an assignment of colors
to V such that in each hyperedge e there
is at least one uniquely-colored vertex. This notion is an extension of the
classical graph coloring. In this talk we are interested in study of this
notion and its applications in the context of frequency assignment to
cellular antennae, in battery consumption aspects of sensor networks, in
RFID protocols and several other fields, and also we survey combinatorial
and algorithmic aspects of this notion.
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