205056734
Hamiltonicity of a Type of Interchange Graphs
Abstract Let R(r1,…, rm) and S(s1,…, sn) be two nonnegative integral vectors, and let U (R,S) denote the class of all m×n matrices of 0's and 1's having row sum vector R and column sum vector S. We prove that if s1s2⋯sn1, the interchange graph G(R,S) of U (R,S) is hamiltonian.
45999842
The number of spanning trees in odd valent circulant graphs
In this paper, we consider the number of spanning trees in circulant graphs. For any class of odd valent circulant graphs C"2"n(a"1,a"2,...,a"k"-"1,n), where a"1,a"2,...,a"k"-"1 are fixed jumps and n varies, some formulas, asymptotic behaviors and linear recurrence relations for the number of its spanning trees are obtained, and some known results on the ones in even valent circulant graphs C"n(a"1,a"2,...,a"k) are improved.
46002685
3-Restricted Edge Connectivity Of Vertex Transitive Graphs
5788058
Heredity of the index of convergence of the line digraph
Let D be a digraph, and let Ln(D) and k(D) denote the nth iterated line digraph of D and the index of convergence of D, respectively. We prove that if D contains neither sources nor sinks, then: (1) k(Ln(D))=k(D)=0 if every connected component of D is a directed cycle. (2) k(Ln(D))=k(D)+n if there exists at least one connected component of D that is not a directed cycle. Finally, we prove that if D has no sources or no sinks then k(D) ≤ k(L(D)) ≤ k(D)+1.
204989114
On the numbers of spanning trees and Eulerian tours in generalized de Bruijn graphs
Abstract In this paper, we give the spectra and characteristic polynomials of generalized de Bruijn graphs. By Tutte's Theorem we can obtain the number of spanning trees and the number of Eulerian tours in such graphs.
195348993
A Riemannian Weighted Filter for Edge-sensitive Image Smoothing
29766053
Construction for bicritical graphs and k-extendable bipartite graphs
A graph G is said to be bicritical if G-u-v has a perfect matching for every choice of a pair of points u and v. Bicritical graphs play a central role in decomposition theory of elementary graphs with respect to perfect matchings. As Plummer pointed out many times, the structure of bicritical graphs is far from completely understood. This paper presents a concise structure characterization on bicritical graphs in terms of factor-critical graphs and transversals of hypergraphs. A connected graph G with at least 2k+2 points is said to be k-extendable if it contains a matching of k lines and every such matching is contained in a perfect matching. A structure characterization for k-extendable bipartite graphs is given in a recursive way. Furthermore, this paper presents an O(mn) algorithm for determining the extendability of a bipartite graph G, the maximum integer k such that G is k-extendable, where n is the number of points and m is the number of lines in G.
41201857
A Note on the Number of Perfect Matchings of Bipartite Graphs
Abstract Let G be a bipartite graph with 2n vertices, A its adjacency matrix and K the number of perfect matchings. For plane bipartite graphs each interior face of which is surrounded by a circuit of length 4s + 2, s ϵ {1, 2, …}, an elegant formula, i.e. det A = (−1)nK2, had been rigorously proved by Cvetkovic et al. (1982). For general bipartite graphs, this note contains a necessary and sufficient condition for the above relation to hold. A fast algorithm to check if a plane bipartite graph has such a relation is given.
1083190
Streaming media caching algorithms for transcoding proxies
Streaming media is expected to become one of the most popular types of Web content in the future. Due to increasing variety of client devices and the range of access speeds to the Internet, multimedia contents may be required to be transcoded to match the client's capability. With transcoding, both the network and the proxy CPU are potential bottlenecks for streaming media delivery. This paper discusses and compares various caching algorithms designed for transcoding proxies. In particular we propose a new adaptive algorithm that dynamically selects an appropriate metric for adjusting the management policy. Experimental results show that the proposed algorithm significantly outperforms those that cache only untranscoded or only transcoded objects. Moreover motivated by the characteristics of many video compression algorithms, we investigate partitioning a video object into sections based on frame type and handling them individually for proxy caching. It is found that partitioning improves performance when CPU power rather than network bandwidth is the limiting resource, particularly when the reference pattern is not highly skewed.
15887745
The Rotation Graphs of Perfect Matchings of Plane Bipartite Graphs
Abstract In the present paper, the minimal proper alternating cycle (MPAC) rotation graph R(G) of perfect matchings of a plane bipartite graph G is defined. We show that an MPAC rotation graph R(G) of G is a directed rooted tree, and thus extend such a result for generalized polyhex graphs to arbitrary plane bipartite graphs. As an immediate result, we describe a one-to-one correspondence between MPAC systems and perfect matchings in G.