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Perfect Graphs and Comparability Graphs
2016The first use of graph theory is dated to 1735. Swiss mathematician and physicist, Leonhard Euler, formulated theorems and definitions related to graphs. Euler was inspired by a real problem regarding crossing bridges in Konigsberg (east Prussia, also known as Krolewiec, Kaliningrad).
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Matching-perfect and cover-perfect graphs
Israel Journal of Mathematics, 1974It is shown that a graphG has all matchings of equal size if and only if for every matching setλ inG, G\V(λ) does not contain a maximal open path of odd length greater than one, which is not contained in a cycle. (V(λ) denotes the set of vertices incident with some edge ofλ.) Subsequently edge-coverings of graphs are discussed.
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Perfect and precisely perfect fuzzy graphs
NAFIPS 2008 - 2008 Annual Meeting of the North American Fuzzy Information Processing Society, 2008In this paper, we consider two different definitions of adjacency in fuzzy graph. Thus any graph theory concept that can be defined through adjacency can have two different variations in fuzzy graph theory. We demonstrate this fact through perfect graph and perfect graph theorem.
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Perfection of glued graphs of perfect original graphs
A graph G is perfect if the chromatic number and the clique number have the same value for every of its induced subgraph. A glued graph results from combining two vertex-disjoint graphs by identifying nontrivial connected isomorphic subgraphs of both graphs. Such subgraphs are referred to as the clones.openaire +1 more source
Fundamentals and developments in fluorescence-guided cancer surgery
Nature Reviews Clinical Oncology, 2021Friso Achterberg +2 more
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A guide to comprehensive phosphor discovery for solid-state lighting
Nature Reviews Materials, 2023Shruti Hariyani +2 more
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Coherent perfect absorbers: linear control of light with light
Nature Reviews Materials, 2017Denis G Baranov +2 more
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Virtually Perfect? Telemedicine for Covid-19
New England Journal of Medicine, 2020Brendan G Carr
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