🚀 go-pugleaf

In next week's (Wed, January 27)

                        S E M I N A R
                             ON
            COMBINATORICS, ALGORITHMS AND GEOMETRY

there will be a talk by

		Hein van der Holst (CWI)
on

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		Nowhere-zero k-flows.

Abstract:
For a directed graph G, a nowhere-zero $k$-flow is defined as a
function $\phi$ on the edges on G such that for
all edges e of G $|\phi(e)|$ is in $1,2,\ldots,k-1$ and
for every vertex v of G
$$\sum_{e \in \delta^+(v)} \phi(e) = \sum_{e \in \delta^-(v)} \phi(e).$$
Tutte (1954) made the following conjecture:
For every directed graph with no isthmus there exist a nowhere-zero $5$-flow.
This is still an open problem but Jaeger(1975) proved that
every directed graph with no isthmus has a nowhere-zero $8$-flow. Seymour
(1981) pushed that value down to $6$, i.e. for
every directed graph with no isthmus there exist a nowhere-zero $6$-flow.
These theorems will be proved in the seminar.   
=============================================================================

Contact Persons: J. Tromp (020 592 4078) and A. Gerards (020 592 4045)
                 (tromp@cwi.nl)              (bgerards@cwi.nl)
Frequency:       2nd and 4th Wednesday of the month
Time:            Wednesday, 14.15-16.00.
Place:           Room M280
                 Centrum voor Wiskunde en Informatica,
                 Kruislaan 413,
                 1098 SJ Amsterdam.