Hamilton cycles and eigenvalues of graphs
WebApr 1, 2005 · A Hamiltonian cycle is a spanning cycle in a graph, i.e., a cycle through every vertex, and a Hamiltonian path is a spanning path. In this paper we present two theorems stating sufficient... WebJul 4, 2024 · In a complete graph, every vertex is adjacent to every other vertex. …
Hamilton cycles and eigenvalues of graphs
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WebLemma 5.3, the eigenvalues of Rare 2, 1 (three times), ... Hamilton cycles in random lifts of graphs, European J. Combin. 27(2006), 1282–1293. [7] P. Chebolu and A.M. Frieze, Hamilton cycles in random lifts of complete directed graphs, SIAM J. Discrete Math. 22(2008), 520–540. WebJun 11, 2024 · By eigenvalues of a graph, we mean the eigenvalues of a certain matrix …
WebApr 1, 2005 · A Hamiltonian cycle is a spanning cycle in a graph, i.e., a cycle through … WebGiven a symmetric n×nmatrix P with 0 ≤ P (u, v) ≤ 1, we define a random graph Gn,P on [n] by independently including any edge {u, v} with probability P (u, v). For k ≥ 1 letAk be the property of containing ⌊k/2⌋ Hamilton cycles, and one perfect matching if k is odd, all edgedisjoint. With an eigenvalue condition on P , and conditions on its row sums, Gn,P …
WebTalks by Krystal Guo. If v is an eigenvector for eigenvalue λ of a graph X and α is an automorphism of X, then α(v) is also an eigenvector for λ. Thus it is ... Webeigenvalues are at most ) and the following conditions are satis ed: 1. d (logn)1+ for some constant >0; 2. logdlog d ˛logn, then the number of Hamilton cycles in Gis n! d n n (1 + o(1))n. 1 Introduction The goal of this paper is to estimate the number of Hamilton cycles in pseudo-random graphs. Putting
WebA Hamiltonian cycle is a closed loop on a graph where every node (vertex) is visited exactly once. A loop is just an edge that joins a node to itself; so a Hamiltonian cycle is a path traveling from a point back to itself, visiting …
WebFeb 16, 2015 · odd path (cycle) of given length, and a Hamilton path (cycle) [9, 15, 18, 19, 23, 24]. In particular, sufficient spectral conditions for the existence of Hamilton paths and cycles receive ... bravia nails oswegoWebApr 1, 2008 · This condition is sharp: the complete bipartite graph T 2 (n) with parts of size ⌊ n / 2 ⌋ and ⌈ n / 2 ⌉ contains no odd cycles and its largest eigenvalue is equal to ⌊ n 2 / 4 ⌋. This condition is stable: if μ ( G ) is close to ⌊ n 2 / 4 ⌋ and G fails to contain a cycle of length t for some t ⩽ n / 321 , then G resembles T 2 ... bravia nasne 再生できないWebA 3-edge-colorable graph is one in which we can color every edge with one of three colors such that at each vertex, all incident edges have di erent colors. The Petersen graph is also the smallest cubic bridgeless graph that does not have a Hamiltonian cycle. Knuth has called the Petersen graph: 1-5 symonides z keos