<span style="font-family:Verdana;">In this paper we analyze and model three open problems posed by Harris, Insko, Prieto-Langarica, Stoisavljevic, and Sullivan in 2020 concerning the tipsy cop and robb...<span style="font-family:Verdana;">In this paper we analyze and model three open problems posed by Harris, Insko, Prieto-Langarica, Stoisavljevic, and Sullivan in 2020 concerning the tipsy cop and robber game on graphs. The three different scenarios we model account for different biological scenarios. The first scenario is when the cop and robber have a consistent tipsiness level through the duration of the game;the second is when the cop and robber sober up as a function of time;the third is when the cop and robber sober up as a function of the distance between them. Using Markov chains to model each scenario we calculate the probability of a game persisting through M rounds of the game and the expected game length given different starting positions and tipsiness levels for the cop and robber.展开更多
The traditional game of cops and robbers is played on undirected graph. Recently, the same game played on directed graph is getting attention by more and more people. We knew that if we forbid some subgraph we can bou...The traditional game of cops and robbers is played on undirected graph. Recently, the same game played on directed graph is getting attention by more and more people. We knew that if we forbid some subgraph we can bound the cop number of the corresponding class of graphs. In this paper, we analyze the game of cops and robbers on H^(-)-free digraphs. However, it is not the same as the case of undirected graph. So we give a new concept(H^(-)^(*)-free digraph) to get a similar conclusion about the case of undirected graph.展开更多
文摘<span style="font-family:Verdana;">In this paper we analyze and model three open problems posed by Harris, Insko, Prieto-Langarica, Stoisavljevic, and Sullivan in 2020 concerning the tipsy cop and robber game on graphs. The three different scenarios we model account for different biological scenarios. The first scenario is when the cop and robber have a consistent tipsiness level through the duration of the game;the second is when the cop and robber sober up as a function of time;the third is when the cop and robber sober up as a function of the distance between them. Using Markov chains to model each scenario we calculate the probability of a game persisting through M rounds of the game and the expected game length given different starting positions and tipsiness levels for the cop and robber.
文摘The traditional game of cops and robbers is played on undirected graph. Recently, the same game played on directed graph is getting attention by more and more people. We knew that if we forbid some subgraph we can bound the cop number of the corresponding class of graphs. In this paper, we analyze the game of cops and robbers on H^(-)-free digraphs. However, it is not the same as the case of undirected graph. So we give a new concept(H^(-)^(*)-free digraph) to get a similar conclusion about the case of undirected graph.
