Burning number of theta graphs
WebFeb 6, 2024 · The burning number of a graph can be used as a simple measure for the speed of the spread of influence in the corresponding social network; the smaller the burning number is, the faster an influence can be spread in the network. Our focus is on a few probabilistic aspects of this problem. Randomness is coming from two possible … WebFeb 13, 2024 · The theta graph ${\Theta _{\ell ,t}}$ consists of two vertices joined by t vertex-disjoint paths, each of length $\ell $ . ... On the Turán Number of Theta Graphs. …
Burning number of theta graphs
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WebJan 17, 2024 · The burning number of a graph G, denoted by bn(G), is the minimum number of rounds required to complete the burning of G. The graph burning problem asks for a burning schedule that completes in bn(G) rounds. Unfortunately, this problem is NP-hard even for simple graphs such as trees or disjoint sets of paths . So, the focus of this … WebMay 30, 2024 · The Turán number ex ( n , H) is the maximum number of edges in any graph of order n that contains no copy of H as a subgraph. For any three positive integers p , q , r with p\le q\le r and q\ge 2, let \theta (p,q,r) denote the graph obtained from three internally disjoint paths with the same pair of endpoints, where the three paths are of ...
WebFeb 16, 2024 · The burning number problem has received considerable attention in recent years and nearly tight upper and lower bounds have been established for various well-known graph classes including generalized Petersen graphs , p-caterpillars , graph products , dense and tree-like graphs and theta graphs . The NP-hardness of the … WebThe burning number of a graph G, denoted by b(G), is the minimum number of rounds needed for the process to end. The parameter b(G) is well-defined, as in a finite ... and theta graphs. Computational complexity results are presented in Section 4. While computing the burning number was known to be NP-complete early on in its …
WebThe burning number b (G) of a graph G was introduced by Bonato, Janssen, and Roshanbin [Lecture Notes in Computer Science 8882 (2014)] to measure the speed of … WebNov 1, 2024 · The graph burning problem is NP-complete even for trees. In this paper, we show that the burning number of any theta graph of order n=q2+r with 1≤r≤2q+1 is …
WebBonato et al. (2014, 2015) defined the burning number of a simple graph as follows. Consider a process called burning involving are discrete time steps. Each node is either burned or unburned; if a node is burned, then it remains in that state until the end of the process. In every round, choose one additional unburned node to burn (if such a node is …
WebMar 20, 2024 · In this paper, we show that the burning number of any theta graph of order n=q2+r with 1≤r≤2q+1 is either q or q+1. … microsoft sql server 2014 iso downloadmicrosoft sql server 2005 + sp2下载WebSep 2, 2024 · In particular, for dense graphs with $\delta \in \Theta(n)$, all vertices are burned in a constant number of rounds. More interestingly, even when $\delta$ is a constant that is independent of the graph size, our algorithm answers the graph-burning conjecture in the affirmative by burning the graph in at most $\lceil \sqrt{n} \rceil$ rounds. microsoft sql server 2014 reporting servicesWebBonato et al. (2014, 2015) defined the burning number of a simple graph as follows. Consider a process called burning involving are discrete time steps. Each node is either … microsoft sql server 2014 express localdb 是什么WebBurning number of theta graphs @article{Liu2024BurningNO, title={Burning number of theta graphs}, author={Huiqing Liu and Ruiting Zhang and Xiaolan Hu}, journal={Appl. Math. Comput.}, year={2024}, volume={361}, pages={246-257} } Huiqing Liu, Ruiting Zhang, Xiaolan Hu; Published 15 November 2024; Mathematics; Appl. Math. Comput. microsoft sql server 2012 setupWebApr 2, 2024 · Burning number of theta graphs. ... The burning number problem on disconnected graphs is harder than on the connected graphs. For example, burning number problem is easy on a path where as it is ... how to create messenger chat roomWebSep 30, 2024 · Very recently, Liu et al. [12] considered the burning number of theta graphs. For more on graph burning and graph searching, see the recent book [6]. In … how to create messy curls