Hamiltonicity in prime sum graphs
 Hamiltonicity in Prime Sum Graphs - ResearchGate)
There are infinitely many Hamiltonian G_{2n}’s. The contribution of this paper is to revisit Conjecture 1, that has stood for decades as an open question, and make progress on it. Our result partly improves the result by Greenfield and Greenfield [10] with new insights from Graph Theory. Although the main result is … See more [10] The set of integers \{1, 2, 3, \cdots , 2n\}, n \ge 1, can be partitioned into pairs \{a_i,b_i\} such that a_i+b_i is prime for all i=1, 2, \cdots , n. … See more [6] The set of integers \{1, 2, 3, \cdots , 2n\}, n \ge 2, can be rearranged in a circle such that the sum of any two adjacent numbers is a prime. In other words, G_{2n}contains a … See more [1, 17] For any positive integer n>1, there is at least a prime p such that n WebFeb 6, 2024 · In this paper, we describe for the first time a nontrivial, naturally arising infinite sequence whose initial segments are all graphic. Furthermore, we show that any realization of the initial segments is admissible for the DPG-algorithm. This sequence is the sequence of prime gaps with a prefix 1:
Hamiltonicity in prime sum graphs
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WebApr 21, 2024 · The domination theory of graphs is an important part of graph theory … WebOct 27, 2024 · It is easy to see that every Hamiltonian graph is connected, has a perfect fractional matching and, excluding the bipartite case, contains an odd cycle. Our main result in turn states that any large enough graph that robustly satisfies these properties must already be Hamiltonian.
WebSometimes, it is easier to work with random Cayley graphs or random Cayley sum graphs for abelian groups, rather than random Latin square graphs. This is because we always have L ij = L−1 ij in the case of Cayley graphs, and L ij = L ji in the case of Cayley sum graphs, and so dependences between the edges can be easier to deal with. WebMar 2, 2024 · A graph is Hamiltonian if it contains a cycle which visits every vertex of the …
WebA Hamiltonian graph, also called a Hamilton graph, is a graph possessing a Hamiltonian … WebSep 1, 1996 · The List Edge Colouring Conjecture asserts that, given any multigraph G with chromatic index k and any set system {S-e:e is an element of E (G)} with each \S-e\ = k, we can choose elements s (e ...
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WebHamiltonicity has been widely studied with relation to various parameters such as graph density, toughness, forbidden subgraphs and distance among other parameters. Dirac and Ore's theorems basically state that a … bolde super cookWebOne approach to designing structured low-density parity-check (LDPC) codes with large girth is to shorten codes with small girth in such a manner that the deleted columns of the parity-check matrix contain all the variables involved in short cycles. gluten free latke recipesWebMay 19, 2016 · In the study of hamiltonicity of graphs, a classical result was proved by Chvátal and Erdös [ 10 ]. Theorem 1.2 (Chvátal and Erdös [ 10 ]) A connected graph G with \alpha (G)\le \kappa (G) is Hamiltonian. For claw-free graphs, Flandrin and Li [ 12] proved the following: Theorem 1.3 gluten free late night snacksgluten free lavash crackersWebAug 24, 2024 · Our main result states that graphs that have a robust Hamilton framework are (in a strong sense) Hamiltonian. As an application we can easily recover many of the above mentioned contributions and also prove several new results. 2 Results To provide an overview of our outcomes, we introduce some further notation. gluten free laxatives to buyWebApr 1, 2024 · Graphs Using the minimum and maximum degrees to bound the diameter of orientations of bridgeless graphs Journal of the Operations Research Society of China Authors: Wan-Ping Zhang Ji-Xiang Meng... gluten free latkes with potato starchWebHamiltonian completion. The Hamiltonian completion problem is to find the minimal … bolde super hoover mercury