Small spectral gap in the combinatorial Laplacian implies Hamiltonian
نویسندگان
چکیده
We consider the spectral and algorithmic aspects of the problem of finding a Hamiltonian cycle in a graph. We show that a sufficient condition for a graph being Hamiltonian is that the eigenvalues of the combinatorial Laplacian are sufficiently close to the average degree of the graph. An algorithm is given for the problem of finding a Hamiltonian cycle in graphs with bounded spectral gaps which has complexity of order nc lnn.
منابع مشابه
Correlation at Low Temperature: I. Exponential Decay
The present paper generalizes the analysis [18, 2] of the correlations for a lattice system of real-valued spins at low temperature. The Gibbs measure is assumed to be generated by a fairly general pair potential (Hamiltonian function). The novelty, as compared to [18, 2], is that the single-site (self-) energies of the spins are not required to have only a single local minimum and no other ext...
متن کاملSIGNLESS LAPLACIAN SPECTRAL MOMENTS OF GRAPHS AND ORDERING SOME GRAPHS WITH RESPECT TO THEM
Let $G = (V, E)$ be a simple graph. Denote by $D(G)$ the diagonal matrix $diag(d_1,cdots,d_n)$, where $d_i$ is the degree of vertex $i$ and $A(G)$ the adjacency matrix of $G$. The signless Laplacianmatrix of $G$ is $Q(G) = D(G) + A(G)$ and the $k-$th signless Laplacian spectral moment of graph $G$ is defined as $T_k(G)=sum_{i=1}^{n}q_i^{k}$, $kgeqslant 0$, where $q_1$,$q_2$, $cdots$, $q_n$ ...
متن کاملSufficient Spectral Conditions for Hamiltonicity
The question of deciding whether or not a given graph is Hamiltonian is a very difficult one; indeed, determining whether a given graph is Hamiltonian is NP-complete. Here, we discuss applications of spectral graph theory to this problem. In particular, we explore results by Fiedler and Nikiforov [2] regarding spectral conditions on the adjacency matrix to ensure Hamiltonicity, and results by B...
متن کاملSome combinatorial aspects of finite Hamiltonian groups
In this paper we provide explicit formulas for the number of elements/subgroups/cyclic subgroups of a given order and for the total number of subgroups/cyclic subgroups in a finite Hamiltonian group. The coverings with three proper subgroups and the principal series of such a group are also counted. Finally, we give a complete description of the lattice of characteristic subgroups of a finite H...
متن کاملSpectral Properties of Yang–mills Theory
Classical Yang–Mills theory in four dimensions is studied by using the Coulomb gauge, as a first step towards considering the mass gap problem in the quantum theory. The Coulomb gauge Hamiltonian involves integration of matrix elements of an operator P which is studied both at perturbative and at non-perturbative level. Upon replacing space-time by a compact Riemannian 4-manifold without bounda...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006