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SEMINARS
Integer flows in Cayley graph
时间  Datetime
2018-11-13 15:30 — 17:00 
地点  Venue
Middle Lecture Room
报告人  Speaker
CUNQUAN ZHANG
单位  Affiliation
West Virginia University
邀请人  Host
张晓东
报告摘要  Abstract

This is a survey talk about Tutte's integer flows in Cayley graphs.
Alspach conjectured that every connected Cayley graph contains a Hamilton cycle.  After almost five decades,
 Alspach's conjecture remains widely open. Note that every Hamiltonian graph admits a nowhere-zero $4$-flow.
The following is a weaker version of Alspach's conjecture (by Alspach, Liu and Z) that
every Cayley graph admits a nowhere-zero $4$-flow (equivalently, there is  no Cayley snarks).
Integer flow theory was introduced by Tutte as a dual version of graph coloring. Tutte proposed several conjectures about integer flows, such as, $3$-, $4$- and $5$-flow conjecture.
The progress of Tutte's conjectures for Cayley graphs will be surveyed  and possible strengthening of
 those early results will be discussed based on
some recent progress in flow theory.