Proof of Alon's Second Eigenvalue Conjecture and Related Problems (eBook)

Joel Friedman (Autor)

eBook Download: PDF

100 Seiten
American Mathematical Society (Verlag)
978-1-4704-0516-8 (ISBN)

Infos

A $d$-regular graph has largest or first (adjacency matrix) eigenvalue $/lambda_1=d$. Consider for an even $d/ge 4$, a random $d$-regular graph model formed from $d/2$ uniform, independent permutations on $/{1,/ldots,n/}$. The author shows that for any $/epsilon>0$ all eigenvalues aside from $/lambda_1=d$ are bounded by $2/sqrt{d-1}/;+/epsilon$ with probability $1-O(n^{-/tau})$, where $/tau=/lceil /bigl(/sqrt{d-1}/;+1/bigr)/2 /rceil-1$. He also shows that this probability is at most $1-c/n^{/tau'}$, for a constant $c$ and a $/tau'$ that is either $/tau$ or $/tau+1$ ("e;more often"e; $/tau$ than $/tau+1$). He proves related theorems for other models of random graphs, including models with $d$ odd.

Produkt-Details

• Themenwelt: Mathematik / Informatik ► Informatik ► Theorie / Studium
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Graphentheorie
• ISBN-10: 1-4704-0516-4 / 1470405164
• ISBN-13: 978-1-4704-0516-8 / 9781470405168