Results 41 to 50 of about 9,193,291 (353)
On degree-sequence characterization and the extremal number of edges for various Hamiltonian properties under fault tolerance [PDF]
Discrete Mathematics & Theoretical Computer Science, 2016 Assume that $n, \delta ,k$ are integers with $0 \leq k < \delta < n$. Given a graph $G=(V,E)$ with $|V|=n$. The symbol $G-F, F \subseteq V$, denotes the graph with $V(G-F)=V-F$, and $E(G-F)$ obtained by $E$ after deleting the edges with at least one ...
Shih-Yan Chen, Shin-Shin Kao, Hsun Su
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, 2012 We generalize the class of split graphs to the directed case and show that these split digraphs can be identified from their degree sequences. The first degree sequence characterization is an extension of the concept of splittance to directed graphs ...
LaMar, M. Drew
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The connectivity of graphs of graphs with self-loops and a given degree sequence [PDF]
J. Complex Networks, 2017 `Double edge swaps' transform one graph into another while preserving the graph's degree sequence, and have thus been used in a number of popular Markov chain Monte Carlo (MCMC) sampling techniques. However, while double edge-swaps can transform, for any
Joel Nishimura
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On factorable degree sequences
Journal of Combinatorial Theory, Series B, 1972 AbstractWe call a degree sequence graphic (respectively, k-factorable, connected k-factorable) if there exists a graph (respectively, a graph with a k-factor, a graph with a connected k-factor) with the given degree sequence. In this paper we give a necessary and sufficient condition for a k-factorable sequence to be connected k-factorable when k ⩾ 2 ...
A Ramachandra Rao, S.B Rao
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On the necessity of Chvátal’s Hamiltonian degree condition
AKCE International Journal of Graphs and Combinatorics, 2020 In 1972 Chvátal gave a well-known sufficient condition for a graphical sequence to be forcibly Hamiltonian, and showed that in some sense his condition is best possible.
Douglas Bauer +3 more
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An Efficient Algorithm to Test Potential Bipartiteness of Graphical Degree Sequences
Theory and Applications of Graphs, 2021 As a partial answer to a question of Rao, a deterministic and customizable efficient algorithm is presented to test whether an arbitrary graphical degree sequence has a bipartite realization.
Kai Wang
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A parallel algorithm for generating a random graph with a prescribed degree sequence [PDF]
2017 IEEE International Conference on Big Data (Big Data), 2017 Random graphs (or networks) have gained a significant increase of interest due to its popularity in modeling and simulating many complex real-world systems. Degree sequence is one of the most important aspects of these systems. Random graphs with a given
Md Hasanuzzaman Bhuiyan +2 more
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The polytope of degree sequences
Linear Algebra and its Applications, 1989 AbstractA nonnegative integer sequence (d1,d2,…,dn) is called a degree sequence if there exists a simple graph on the vertex set V= {1,2,…,n} such that deg(i)= di for all i. The degree sequence of a threshold graph is a threshold sequence. Let Dn= Convex Hull {(x1,x2,…,xn)|(x1,…,xn) is a degree sequence}.
Murali K. Srinivasan, Uri N. Peled
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Canonical horizontal visibility graphs are uniquely determined by their degree sequence [PDF]
, 2016 Horizontal visibility graphs (HVGs) are graphs constructed in correspondence with number sequences that have been introduced and explored recently in the context of graph-theoretical time series analysis. In most of the cases simple measures based on the
B. Luque, L. Lacasa
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The second order degree sequence problem is NP-complete [PDF]
arXiv.org, 2016 The classical degree sequence problems for simple graphs are computationally easy. In the last years numerous new construction problems were introduced (for example the joint degree matrix problems and its variants) which are still easy.
P. Erdös, I. Miklós
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