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SEMINAR: Groups and Combinatorics Seminar: Several open problems in graph theory

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Groups and Combinatorics Seminar

Mehdi Behzad, Sharif University, Tehran

will speak on

Several open problems in graph theory

at 2pm Friday 16th July in MLR2

(**Note the different time to usual***)

The speaker is also giving a Colloquium at 12 noon on Tuesday.

Abstract: The author's Ph.D. thesis [1] contains the Total Chromatic Number Conjecture which is still unsettled. Reference [3] introduces the Total Ramsey Numbers R"(r,s) for positive integers r and s, and provides the exact values of this function for all the lattice points outside the region {(r,s): r > 4, s > r 2-5r+8}.

In this informal talk, we first elaborate on the above old problems. Then, we introduce several classes of new problems in relation to a fiction entitled, `The Story of the King and the Mathematician.' Each new problem, presented in the context of a puzzle, is about dismantling, displacing, and reconstructing an arbitrary graph G [2].

Based on the fiction, the first class of the new problems is generalized to obtain the second class. Each member of the latter class introduces several new puzzles with different levels of difficulties. Next, we assign a weight function to the vertex set of the graph involved in each puzzle. One such weight function produces the second class. Hence, this third class is a generalization of the second as well as the first class. Finally, we dismantle, displace, and reconstruct the weighted graph G with prescribed conditions.

In order to solve each puzzle, weneed to obtain the values of a few parameters, provide a procedure to find all the annihilating subsets of the vertex set of the graph G, and find an algorithm to transfer G with pre-assigned conditions.

REFERENCES:

[1] M. Behzad, Graphs and their Chromatic Numbers, Doctoral Thesis, Michigan State University (1965).

[2] M. Behzad, Dismantling, Displacing and Reconstructing Graphs, Manuscript (2009).

[3] M. Behzad and H. Radjavi, Another analogue of Ramsey Numbers, Math. Annal.186, 228 - 232 (1970).



All Welcome.
Speaker(s) Mehdi Behzad
Location Maths Lecture Room 2
Contact Michael Giudici <[email protected]>
Start Fri, 16 Jul 2010 14:00
End Fri, 16 Jul 2010 14:45
Submitted by Michael Giudici <[email protected]>
Last Updated Tue, 13 Jul 2010 08:17
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