Tag: graph theory
Graph editor and Matrix generator
Making matrix representations of graphs always takes a lot of time. For practicing algebraic or spectral graph theory on computer algebra systems, one has to create a lot of graphs. A handy tool can make this easy, which allows to draw graphs and generate code e.g. for Maple with one click. Well I couldn’t find a tool like that, so I made one on the weekend in C#. With it, you can draw custom graphs, including: arbitrary loops, parallel edges, directed edges, etc. and can generate code for these computer algebra systems: Maple, MATLAB, Maxima. Then the code can be
Deadlocks and graph theory
When accessing a database through a series of transactions, a deadlock can occur any time. They are natural companions of transactions. We can decrease their likelihood by rigorously accessing the records and the tables always in the same order, but over a level of complexity we can never be 100% free of them. This is a fair price for the ACID properties. Deadlocks occur very rarely, and when this happens, the only thing to do is to repeat the transaction in the process which had been interrupted by the deadlock detection demon of the database. This is very small performance
An interesting proof of Turán’s theorem
In the past few days I have been reading a nice book about graph theory, including solving the exercises in it. Once I encountered an exercise which I couldn’t solve, so made a little research, and found that the solution is the proof of the Turán’s theorem. The usual proof for this theorem is built on induction, but later I have found a proof which is using a basic inequality. I am sure that I’m not the first one who have seen this solution, although I couldn’t find it on the net yet.
