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Collapsible Graphs and Hamiltonicity of Line Graphs
Graphs and Combinatorics, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yang, Weihua +3 more
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Discrete Mathematics, 2022
A connected graph is said to be supereulerian if it containes a spanning Eulerian subgraph. The interest in these graphs comes from the fact that such a graph has a Hamiltonian line graph. A graph \(G\) is called essentially \(k\)-edge connected if \(G\) does not have an essential edge cut \(X\) with \(|X| < k.\) The main results of this paper ...
Yingmin Shangguan, Liming Xiong
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A connected graph is said to be supereulerian if it containes a spanning Eulerian subgraph. The interest in these graphs comes from the fact that such a graph has a Hamiltonian line graph. A graph \(G\) is called essentially \(k\)-edge connected if \(G\) does not have an essential edge cut \(X\) with \(|X| < k.\) The main results of this paper ...
Yingmin Shangguan, Liming Xiong
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Graphs and Combinatorics, 1994
``For integers \(k \geq 2\), the \(k\)-line graph of a graph \(G\) is defined as a graph whose vertices correspond to the complete subgraphs on \(k\) vertices in \(G\) with two distinct vertices adjacent if the corresponding complete subgraphs have \(k-1\) common vertices in \(G\).'' Starting with a graph \(G\), one can construct the sequence of graphs
Van Bang Le, Erich Prisner
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``For integers \(k \geq 2\), the \(k\)-line graph of a graph \(G\) is defined as a graph whose vertices correspond to the complete subgraphs on \(k\) vertices in \(G\) with two distinct vertices adjacent if the corresponding complete subgraphs have \(k-1\) common vertices in \(G\).'' Starting with a graph \(G\), one can construct the sequence of graphs
Van Bang Le, Erich Prisner
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Journal of Graph Theory, 1984
AbstractWe give best possible Ore‐like conditions for a graph so that its line graph is Hamiltonian.
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AbstractWe give best possible Ore‐like conditions for a graph so that its line graph is Hamiltonian.
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Acta Mathematicae Applicatae Sinica, English Series, 2021
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Yang, Wei-ling +2 more
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Yang, Wei-ling +2 more
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Communications in Nonlinear Science and Numerical Simulation, 2017
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Wiktor Warchalowski +1 more
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Wiktor Warchalowski +1 more
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Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference, 2009
In this paper we investigate discrete linear search and graph search problems. It is well-known that the Bounded Discrete Linear Search Problem (BDLSP) can be solved efficiently using a dynamic programming approach. However, we show that its generalization to the graph case—the Graph Search Problem (GSP)—is NP-complete. We further consider the Discrete
Hua Li, Edwin K. P. Chong
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In this paper we investigate discrete linear search and graph search problems. It is well-known that the Bounded Discrete Linear Search Problem (BDLSP) can be solved efficiently using a dynamic programming approach. However, we show that its generalization to the graph case—the Graph Search Problem (GSP)—is NP-complete. We further consider the Discrete
Hua Li, Edwin K. P. Chong
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Pattern Recognition Letters, 1993
The author defines and studies the concept of a fuzzy line graph of a fuzzy graph. The necessary and sufficient conditions for a fuzzy graph to be isomorphic to its corresponding fuzzy line graph are given. Also established is a necessary and sufficient condition for a fuzzy graph to be a fuzzy line graph of a fuzzy graph.
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The author defines and studies the concept of a fuzzy line graph of a fuzzy graph. The necessary and sufficient conditions for a fuzzy graph to be isomorphic to its corresponding fuzzy line graph are given. Also established is a necessary and sufficient condition for a fuzzy graph to be a fuzzy line graph of a fuzzy graph.
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A characterization of graphs with supereulerian line graphs
International Journal of Computer Mathematics: Computer Systems Theory, 2020The line graph L(G) of a graph G is a simple graph with E(G) being its vertex set, where two vertices are adjacent in L(G) whenever the corresponding edges share a common vertex in G.
Yufei Huang 0007 +4 more
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Acta Mathematica Scientia, 1998
For a graph \(G\), let \(\overline {\sigma}_2\) denote min\(\{ d(u) + d(v)\mid uv \in E(G) \}\). The author shows that if \(G\) is connected and of order \(n \geq 43\) such that the line graph \(L(G)\) is Hamiltonian and \(\overline {\sigma}_2> 2(n/5 - 1)\), then \(L(G)\) is pancyclic. This settles a conjecture of Benhocine et al. For a connected graph
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For a graph \(G\), let \(\overline {\sigma}_2\) denote min\(\{ d(u) + d(v)\mid uv \in E(G) \}\). The author shows that if \(G\) is connected and of order \(n \geq 43\) such that the line graph \(L(G)\) is Hamiltonian and \(\overline {\sigma}_2> 2(n/5 - 1)\), then \(L(G)\) is pancyclic. This settles a conjecture of Benhocine et al. For a connected graph
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