Hello, I am a third year undergraduate in CS. I am eager to pursue higher education from one of the best institutes in out country. For that I need to write a competitive exam, named GATE which had this syllabus for this year 2021. The syllabus remains more or less the same each and every year.
The pattern is as follows, 65 questions , time 3 hours. So for each question, I can afford at most 2.76 mins, which is quite a constrained amount of time, considering the level of the questions.
This is to give an idea about the level of the questions
As per the given syllabus, the exam asks quite involving questions on Graph Theory, with questions based on properties of graph algorithms, tree formed by traversals, or coloring or other important but at times unseen (by the candidates) properties or concepts. Mostly they tend to ask questions from unseen topics, which probably one has not handled previously unless he is quite lucky. In such cases they definite the topics and then asks on them.
Usually questions are like select the most appropriate options or marking the true statements.
Now it is quite difficult (for me at least) to understand in 2.76 mins the new concept (defined in the question), read the statements, find counter examples for them to prove them wrong. At worse for some statements it might happen, that I am unable to find the counter example in that 2.76 mins of time, but it might happen that a more difficult counter example might exist.
One can have a look at the type of question in graph theory here and here and here.
I have gone through CLRS and I am acquainted with the terminologies or graph theory algorithms and properties of tree produced by traversals etc. But the thing is that all these I have learnt, by going through the text many times and I have been quite slow at grasping those concepts given in CLRS.I have even gone to Kenneth Rosen's Discrete Mathematics texts. As per the recommendations given in few coaching institutes (note that I do not go to any one of them, I do self study, got to know from my classmate), I have picked up Narsingh Deo's Graph Theory text and I am going through it now.
[I have solved most of the exercise questions of CLRS (except for the $\star$ questions) mostly on my own but only for once, long a ago, while reading the text for the first time. Some questions even took a single day to think (too slow indeed). Rosen has a huge no of questions at the end of each text, that too I have solved not all but selectively as I found few problems repetitive there, and that too I have done only once. But I have read the text many more times (that too selectively), so that I do not forget the things which I have learnt...]
Could anyone recommend me some good text or detailed video lecture series (not a very advanced one) that would help me to build intuition behind graph theory properties or statements unknown to me. The texts which I have already read are classic and fine, but I find it difficult at times to answer questions in the GATE, (might be due to the short time or might be that I am not that sharp) but still I want to sharpen my skills in dealing with these problems of graph theory. Even the weightage of this subject is quite high every year.