Facial unique-maximum colorings of plane graphs with restriction on big vertices

Lidický, Bernard; Messerschmidt, Kacy; Škrekovski, Riste

doi:10.1016/j.disc.2019.05.029

Cited by 3 publications

(3 citation statements)

References 8 publications

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“…At the beginning of this method, the variables FoundSolution, terminated, recursions, and the local variable Iteration are initialized. The local variable Iteration controls the construction repeat-until (lines [9][10][11][12][13][14][15][16][17][18][19]. Through this construction, the idea of the algorithm to check whether the given graph can be colored with 1, 2, 3, ..., and VertexCount colors is realized.…”

Section: Methodsmentioning

confidence: 99%

“…Scientific publications have described many variants of this problem. For instance, the reconfiguration graph for vertex colorings of weakly chordal graphs [16], the facial unique-maximum colorings of plane graphs with restriction on big vertices [17], the vertex coloring with communication constraints in synchronous broadcast networks [18], and other. Different variants use different approaches [19], [20], techniques [21], [22] and algorithms [23], [24].…”

Section: Introductionmentioning

confidence: 99%

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An analysis between different algorithms for the graph vertex coloring problem

Kralev

Kraleva

2023

IJECE

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<span lang="EN-US">This research focuses on an analysis of different algorithms for the graph vertex coloring problem. Some approaches to solving the problem are discussed. Moreover, some studies for the problem and several methods for its solution are analyzed as well. An exact algorithm (using the backtracking method) is presented. The complexity analysis of the algorithm is discussed. Determining the average execution time of the exact algorithm is consistent with the multitasking mode of the operating system. This algorithm generates optimal solutions for all studied graphs. In addition, two heuristic algorithms for solving the graph vertex coloring problem are used as well. The results show that the exact algorithm can be used to solve the graph vertex coloring problem for small graphs with 30-35 vertices. For half of the graphs, all three algorithms have found the optimal solutions. The suboptimal solutions generated by the approximate algorithms are identical in terms of the number of colors needed to color the corresponding graphs. The results show that the linear increase in the number of vertices and edges of the analyzed graphs causes a linear increase in the number of colors needed to color these graphs.</span>

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An analysis between different algorithms for the graph vertex coloring problem

Kralev

Kraleva

2023

IJECE

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“…While the majority of the research is based on the acyclic graph, there are few researches on specialized graph such as edge coloring [29] and plane graph [30,31]. One of the specialized edge coloring is rainbow coloring [32] that is when the triangular graph has three unique edge colors, and few researches provide proof for rainbow coloring [33].…”

Section: Without Social Distancingmentioning

confidence: 99%

Analysis on COVID-19 Infection Spread Rate during Relief Schemes Using Graph Theory and Deep Learning

Palanivinayagam

Panneerselvam

Kumar

et al. 2022

Computational and Mathematical Methods in Medicine

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The novel coronavirus 2019 (COVID-19) disease is a pandemic which affects thousands of people throughout the world. It has rapidly spread throughout India since the first case in India was reported on 30 January 2020. The official report says that totally 4, 11,773 cases are positive, 2, 28,307 recovered, and the country reported 12,948 deaths as of 21 June 2020. Vaccination is the only way to prevent the spreading of COVID-19 disease. Due to various reasons, there is vaccine hesitancy across many people. Hence, the Indian government has the solution to avoid the spread of the disease by instructing their citizens to maintain social distancing, wearing masks, avoiding crowds, and cleaning your hands. Moreover, lots of poverty cases are reported due to social distancing, and hence, both the center government and the respective state governments decide to issue relief funds to all its citizens. The government is unable to maintain social distancing during the relief schemes as the population is huge and available support staffs are less. In this paper, the proposed algorithm makes use of graph theory to schedule the timing of the relief funds so that with the available support staff, the government would able to implement its relief scheme while maintaining social distancing. Furthermore, we have used LSTM deep learning model to predict the spread rate and analyze the daily positive COVID cases.

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