edge partition
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2019 ◽  
Vol 17 (1) ◽  
pp. 81-87 ◽  
Author(s):  
Lina Zheng ◽  
Yiqiao Wang ◽  
Wei Gao

AbstractA large number of medical experiments have confirmed that the features of drugs have a close correlation with their molecular structure. Drug properties can be obtained by studying the molecular structure of corresponding drugs. The calculation of the topological index of a drug structure enables scientists to have a better understanding of the physical chemistry and biological characteristics of drugs. In this paper, we focus on Hyaluronic Acid-Paclitaxel conjugates which are widely used in the manufacture of anticancer drugs. Several topological indices are determined by virtue of the edge-partition method, and our results remedy the lack of medicine experiments, thus providing a theoretical basis for pharmaceutical engineering.


2019 ◽  
Vol 39 (3) ◽  
pp. 383-393
Author(s):  
Meihua Meihua ◽  
Meiling Guan ◽  
Jirimutu Jirimutu

We use the Katona-Kierstead definition of a Hamiltonian cycle in a uniform hypergraph. A decomposition of complete \(k\)-uniform hypergraph \(K^{(k)}_{n}\) into Hamiltonian cycles was studied by Bailey-Stevens and Meszka-Rosa. For \(n\equiv 2,4,5\pmod 6\), we design an algorithm for decomposing the complete 3-uniform hypergraphs into Hamiltonian cycles by using the method of edge-partition. A decomposition of \(K^{(3)}_{n}\) into 5-cycles has been presented for all admissible \(n\leq17\), and for all \(n=4^{m}+1\) when \(m\) is a positive integer. In general, the existence of a decomposition into 5-cycles remains open. In this paper, we show if \(42~|~(n-1)(n-2)\) and if there exist \(\lambda=\frac{(n-1)(n-2)}{42}\) sequences \((k_{i_{0}},k_{i_{1}},\ldots,k_{i_{6}})\) on \(D_{all}(n)\), then \(K^{(3)}_{n}\) can be decomposed into 7-cycles. We use the method of edge-partition and cycle sequence. We find a decomposition of \(K^{(3)}_{37}\) and \(K^{(3)}_{43}\) into 7-cycles.


2018 ◽  
Vol 333 ◽  
pp. 480-489
Author(s):  
Yiqiao Wang ◽  
Weifan Wang ◽  
Ying Wang

2017 ◽  
Vol 45 (1) ◽  
pp. 6-6
Author(s):  
Lingda Li ◽  
Robel Geda ◽  
Ari B. Hayes ◽  
Yanhao Chen ◽  
Pranav Chaudhari ◽  
...  

Author(s):  
Lingda Li ◽  
Robel Geda ◽  
Ari B. Hayes ◽  
Yanhao Chen ◽  
Pranav Chaudhari ◽  
...  

2017 ◽  
Vol 5 (1) ◽  
pp. 117-131
Author(s):  
K. Pravas ◽  
◽  
A. Vijayakumar ◽  
Keyword(s):  

2016 ◽  
Vol Vol. 17 no. 3 (Graph Theory) ◽  
Author(s):  
Julien Bensmail ◽  
Brett Stevens

International audience A graph is locally irregular if every two adjacent vertices have distinct degrees. Recently, Baudon et al. introduced the notion of decomposition into locally irregular subgraphs. They conjectured that for almost every graph $G$, there exists a minimum integer $\chi^{\prime}_{\mathrm{irr}}(G)$ such that $G$ admits an edge-partition into $\chi^{\prime}_{\mathrm{irr}}(G)$ classes, each of which induces a locally irregular graph. In particular, they conjectured that $\chi^{\prime}_{\mathrm{irr}}(G) \leq 3$ for every $G$, unless $G$ belongs to a well-characterized family of non-decomposable graphs. This conjecture is far from being settled, as notably (1) no constant upper bound on$\chi^{\prime}_{\mathrm{irr}}(G)$ is known for $G$ bipartite, and (2) no satisfactory general upper bound on $\chi^{\prime}_{\mathrm{irr}}(G)$ is known. We herein investigate the consequences on this question of allowing a decomposition to include regular components as well. As a main result, we prove that every bipartite graph admits such a decomposition into at most $6$ subgraphs. This result implies that every graph $G$ admits a decomposition into at most $6(\lfloor \mathrm{log} \chi (G) \rfloor +1)$ subgraphs whose components are regular or locally irregular.


10.37236/2534 ◽  
2015 ◽  
Vol 22 (4) ◽  
Author(s):  
Evan Morgan ◽  
Bogdan Oporowski

If $X$ is a collection of edges in a graph $G$, let $G/X$ denote the contraction of $X$. Following a question of Oxley and a conjecture of Oporowski, we prove that every projective planar graph $G$ admits an edge partition $\{X,Y\}$ such that $G/X$ and $G/Y$ have tree-width at most three. We prove that every toroidal graph $G$ admits an edge partition $\{X,Y\}$ such that $G/X$ and $G/Y$ have tree-width at most three and four, respectively.


2014 ◽  
Vol 672-674 ◽  
pp. 1935-1939
Author(s):  
Guan Ru Li ◽  
Yi Ming Lei ◽  
Jirimutu

About the Katona-Kierstead definition of a Hamiltonian cycles in a uniform hypergraph, a decomposition of complete k-uniform hypergraph Kn(k) into Hamiltonian cycles studied by Bailey-Stevens and Meszka-Rosa. For n≡2,4,5 (mod 6), we design algorithm for decomposing the complete 3-uniform hypergraphs into Hamiltonian cycles by using the method of edge-partition. A decomposition of Kn(3) into 5-cycles has been presented for all admissible n≤17, and for all n=4m +1, m is a positive integer. In general, the existence of a decomposition into 5-cycles remains open. In this paper, we use the method of edge-partition and cycle sequence proposed by Jirimutu and Wang. We find a decomposition of K20(3) into 5-cycles.


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