Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4602729 | Linear Algebra and its Applications | 2008 | 7 Pages |
Abstract
Let G be a graph of sufficiently large order n, and let the largest eigenvalue μ(G) of its adjacency matrix satisfies . Then G contains a cycle of length t for every t⩽n/320This condition is sharp: the complete bipartite graph T2(n) with parts of size ⌊n/2⌋ and ⌈n/2⌉ contains no odd cycles and its largest eigenvalue is equal to .This condition is stable: if μ(G) is close to and G fails to contain a cycle of length t for some t⩽n/321, then G resembles T2(n).
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory