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Showing 1 to 4 of 4 for “"Ramanujan graphs"”.
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Bounds on k-Regular Ramanujan Graphs and Separator Theorems
Expander graphs are a family of graphs that are highly connected. Finding explicit examples of expander graphs which are also sparse is a difficult problem. The best type of expander graph in a. certain sense is a Ramanujan graph. Families of graphs that have separator theorems fail to be Ramanujan …
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The Expanding Constant, Ramanujan Graphs, and Winnie Li Graphs
… foundations for the construction of Winnie Li's graphs and for the proof that Winnie Li's graphs are Ramanujan. The paper also establishes the implications of the Ramanujan property for the expanding constant.
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Good families of quantum low-density parity-check codes and a geometric framework for the amplitude-damping channel
… from embeddings of the Lubotzky-Phillips-Sarnak Ramanujan graphs. These families of quantum error-correcting codes answer a conjecture proposed by MacKay about the existence of good families of quantum low-density parity-check codes with nonzero rate, increasing minimum distance and a practical …
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Unique Games Conjecture : the Boolean Hypercube and connections to graph lifts
… the behaviour of the SDP on general families of graphs. As a quick corollary we establish that the SDP is exact for planar graphs. The second question is concerned with spectrum of label extended graphs of Unique Games instances. Such graphs have been extensively studied under the name of Graph …