Catherine Greenhill the Cycle Double Cover Conjecture
نویسنده
چکیده
In the year 2000, exactly one hundred years after David Hilbert posed his now famous list of 23 open problems, The Clay Mathematics Institute (CMI) announced its seven Millennium Problems. (http://www. claymath.org/millennium). The Gazette has asked leading Australian mathematicians to put forth their own favourite ‘Millennium Problem’. Due to the Gazette’s limited budget, we are unfortunately not in a position to back these up with seven-figure prize monies, and have decided on the more modest 10 Australian dollars instead. In this issue Catherine Greenhill will explain her favourite open problem that should have made it to the list.
منابع مشابه
On the oriented perfect path double cover conjecture
An oriented perfect path double cover (OPPDC) of a graph $G$ is a collection of directed paths in the symmetric orientation $G_s$ of $G$ such that each arc of $G_s$ lies in exactly one of the paths and each vertex of $G$ appears just once as a beginning and just once as an end of a path. Maxov{'a} and Ne{v{s}}et{v{r}}il (Discrete Math. 276 (2004) 287-294) conjectured that ...
متن کاملOn a conjecture of Keedwell and the cycle double cover conjecture
At the 16th British Combinatorial Conference (1997), Cameron introduced a new concept called 2-simultaneous coloring. He used this concept to reformulate a conjecture of Keedwell (1994) on the existence of critical partial latin squares of a given type. Using computer programs, we have veri ed the truth of the above conjecture (the SE conjecture) for all graphs having less than 29 edges. In thi...
متن کاملDirected cycle double covers and cut-obstacles
A directed cycle double cover of a graph G is a family of cycles of G, each provided with an orientation, such that every edge of G is covered by exactly two oppositely directed cycles. Explicit obstructions to the existence of a directed cycle double cover in a graph are bridges. Jaeger [4] conjectured that bridges are actually the only obstructions. One of the difficulties in proving the Jaeg...
متن کاملNowhere zero flows in line graphs
Cai an Corneil (Discrete Math. 102 (1992) 103–106), proved that if a graph has a cycle double cover, then its line graph also has a cycle double cover, and that the validity of the cycle double cover conjecture on line graphs would imply the truth of the conjecture in general. In this note we investigate the conditions under which a graph G has a nowhere zero kow would imply that L(G), the line...
متن کاملEven cycle decompositions of 4-regular graphs and line graphs
An even cycle decomposition of a graph is a partition of its edge into even cycles. We first give some results on the existence of even cycle decomposition in general 4-regular graphs, showing that K5 is not the only graph in this class without such a decomposition. Motivated by connections to the cycle double cover conjecture we go on to consider even cycle decompositions of line graphs of 2-c...
متن کامل