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Sep
19 |
comment |
Value of “of course” in the mathematical literature
I think anybody who has graded undergraduate analysis assignments has said that at least once. |
Sep
19 |
comment |
Smallest non-isomorphic strongly regular graphs
Thanks for the clarification, David. Do you know if they are indeed the smallest, as they seem to be? |
Sep
19 |
answered | Smallest non-isomorphic strongly regular graphs |
Sep
19 |
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Bounds on strong vertex colourings of regular hypergraphs?
As you probably realize, this is equivalent to colouring the graph that you get by replacing the hyperedges with cliques. Doing this gives you an upper bound of $k(\omega-1)+1$ if the hypergraph has maximum edge size $\omega$, by Brooks' Theorem. That's a pretty lousy bound, though, and I imagine you can do better. |
Sep
16 |
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What introductory book on Graph Theory would you recommend?
I was starting to think nobody would mention it! |
Sep
7 |
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Does every triangle-free graph with maximum degree at most 6 have a 5-colouring?
Good question; it is known to hold, without the round-up. Reed never published the result in a paper but it's in Graph Colouring and the Probabilistic Method (with Molloy), in the chapter on hard-core distributions (Chapter 23 I think). (It wouldn't let me comment twice in a row, so I deleted the old comment to add: ) A proof of a stronger result, noted by McDiarmid, appears in Section 2.2 of my thesis, which is here: columbia.edu/~ak3074/papers/phdthesis.pdf |
Sep
7 |
awarded | Nice Question |
Sep
6 |
comment |
Covering of a graph via independent sets
In that case I would consider how to ask the question in terms of hypergraphs and ask a question in this context. I'm confident somebody will know a better bound than $\Delta+1$. See, for example, this conjecture: garden.irmacs.sfu.ca/?q=op/a_generalization_of_vizings_theorem |
Sep
6 |
revised |
Does every triangle-free graph with maximum degree at most 6 have a 5-colouring?
removed latex from title |
Sep
6 |
awarded | Student |
Sep
6 |
asked | Does every triangle-free graph with maximum degree at most 6 have a 5-colouring? |
Sep
4 |
answered | Covering of a graph via independent sets |
Sep
2 |
answered | What are your favorite instructional counterexamples? |
Sep
2 |
comment |
Lower bounds for chromatic number of a graph
By the way, you mention the Kneser graph. This is one graph class that can be used as a nasty example showing that the chromatic number is not necessarily upper-bounded by any function of the fractional chromatic number, meaning that in the worst case, the fractional chromatic number will give you a really lousy approximation. |
Sep
2 |
answered | Lower bounds for chromatic number of a graph |
Sep
2 |
awarded | Supporter |
Mar
12 |
awarded | Editor |
Mar
12 |
revised |
Chromatic number of graphs of tangent closed balls
grammar |
Mar
12 |
awarded | Autobiographer |
Mar
12 |
awarded | Teacher |