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Full-Text Articles in Other Mathematics
Ultrametrics And Complete Multipartite Graphs, Viktoriia Viktorivna Bilet, Oleksiy Dovgoshey, Yuriy Nikitovich Kononov
Ultrametrics And Complete Multipartite Graphs, Viktoriia Viktorivna Bilet, Oleksiy Dovgoshey, Yuriy Nikitovich Kononov
Theory and Applications of Graphs
Let (X, d) be a semimetric space and let G be a graph. We say that G is the diametrical graph of (X, d) if X is the vertex set of G and the adjacency of vertices x and y is equivalent to the equality diam X = d(x, y). It is shown that a semimetric space (X, d) with diameter d* is ultrametric if the diametrical graph of (X, d ε) with d ε (x, y) = min{d(x, y), ε} is complete multipartite for every ε ∈ (0, d* …
How To Guard An Art Gallery: A Simple Mathematical Problem, Natalie Petruzelli
How To Guard An Art Gallery: A Simple Mathematical Problem, Natalie Petruzelli
The Review: A Journal of Undergraduate Student Research
The art gallery problem is a geometry question that seeks to find the minimum number of guards necessary to guard an art gallery based on the qualities of the museum’s shape, specifically the number of walls. Solved by Václav Chvátal in 1975, the resulting Art Gallery Theorem dictates that ⌊n/3⌋ guards are always sufficient and sometimes necessary to guard an art gallery with n walls. This theorem, along with the argument that proves it, are accessible and interesting results even to one with little to no mathematical knowledge, introducing readers to common concepts in both geometry and graph …