Burning number of theta graphs
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. … 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 …
Burning number of theta graphs
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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 ... WebNov 14, 2024 · The 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 the spread of contagion in a graph. The graph burning problem is NP-complete even for trees. In this paper, we show that the burning number of any theta graph of …
WebApr 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 ... WebWe consider graph burning on binomial random graphs, generalized Petersen graphs, 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 formulation, a number of newer results have been discovered.
WebMay 20, 2024 · Graph burning is a process of information spreading through the network by an agent in discrete steps. The problem is to find an optimal sequence of nodes that have to be given information so that the network is covered in least number of steps. Graph burning problem is NP-Hard for which two approximation algorithms and a few … 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 …
WebIn this paper we examine k-burning number for a graph, which generalizes the burning number by allowing to directly burn k unburnt vertices at each round; see Figure 1(b). Throughout the paper, we use the notation b k(G) to denote the k-burning number of a graph G. Note that in the case when k = 1, the 1-burning number b 1(G) coincides with …
WebSep 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 … pink coloring sheets for preschoolersWebMar 20, 2024 · New heuristics for burning graphs. The concept of graph burning and burning number (bn (G)) of a graph G was introduced recently [1]. Graph burning … pink color in semenWebFeb 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 … pink color in photoshopWebarXiv:2003.09314v1 [cs.DM] 20 Mar 2024 Keywords burning number, heuristic, distance to cluster, theta graphs, DIMACS, ... 1 Introduction Burning number of a graph is a new … pink color in pot while fryingWebtractable algorithm to compute burning number parameterized by neighborhood diversity, and showed that for cographs and split graphs the burning number can be computed in polynomial time. Bonato and Kamali [9] showed that the burning number of a graph is approximable within a factor of 3 for general graphs and 2 for trees. pink coloring pages for preschoolWebNov 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 … pink coloring worksheetWebin Section 4, we turn to the complexity of the graph burning problem in directed graphs. We show that the problem is NP-hard for directed trees with one indegree-0 node, but solvable in FPT time; and for DAGs, we show that the problem is W[2]-hard. We nish this section with an algorithm for digraph burning. Finally, in Section 5, we discuss the ... pink color in html