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Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.

2 votes
2 answers
409 views

Lovasz theta function - uses

Lovasz theta function bounds the Shannon capacity of graphs. What are some other uses of the function - especially in asymptotic coding theory and optimization problems?
25 votes
3 answers
2k views

Interpretations and models of permanent

The standard interpretation of permanent of a $0/1$ matrix if considered as a biadjacency matrix of a bipartite graph is number of perfect matchings of the graph or if considered as a adjacency matrix …
18 votes
8 answers
2k views

Concepts in topology successfully transferred to graph theory and combinatorics with non-tri...

What are some of the difficult concepts in topology that have been transferred to graph theory and combinatorics where a certain new application has been found. A good example is Lovász's proof of Kn …
8 votes
1 answer
978 views

Steps in Geometric Complexity Theory

GCT purports to provide a program to show that $NP \not \subset P/poly$. At the high level what are the steps involved in the program and what stage is each step in? What difficulties currently ar …
1 vote
0 answers
40 views

Necessary additive and multiplicative properties to characterize a mildly growing function

Given $k>1$ what could be the necessary additive and multiplicative property of the minimum smooth growing monotone function $f:\Bbb R\rightarrow\Bbb R$ needed such that $\forall a\geq 2^k+1$ we have …
6 votes
3 answers
422 views

Repository of graph classes that are tough to test non-isomorphic pairs from isomorphic pairs

(1) Which graph classes are extremely tough to test for graph non-isomorphic pairs from isomorphic pairs? (2) Is there a repository of adjacencies from such classes?
5 votes
2 answers
837 views

Database of adjacency matrices on cospectral non-isomorphic graph pairs

Is there a repository of cospectral non-isomorphic graphs available somewhere? I am looking for list of $0/1$ adjacency matrix pairs that can be input data in tools such as MATLAB.