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Neighbor‐connected graphs and projective planes
Networks, 1987AbstractIn [G. Gunther, Neighbor‐connectivity in regular graphs. Discrete Appl. Math. 11 (1985) 233–243] Gunther introduced the concept of a k neighbor‐connected graph, which has the property that the removal of any k − 1 closed neighborhoods neither disconnects the graph, nor leaves only a complete graph.
Gunther, G. +2 more
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SIAM Journal on Computing, 1999
Plane graphs \(G\) can be represented by floor plans. A floor plan is a rectangle, partitioned into a set of disjoint rectilinear polygonal regions, which are called the modules. Every module presents a vertex, and it is required that two modules share a piece of their borders if and only if the corresponding vertices are adjacent in \(G\). It has been
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Plane graphs \(G\) can be represented by floor plans. A floor plan is a rectangle, partitioned into a set of disjoint rectilinear polygonal regions, which are called the modules. Every module presents a vertex, and it is required that two modules share a piece of their borders if and only if the corresponding vertices are adjacent in \(G\). It has been
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1992
Planar graphs have many important applications in computer science, for example in VLSI layout. Many problems that are hard or even NP-complete for arbitrary graphs are much easier for planar graphs. In the next lecture we will prove a nice result due to Lipton and Tarjan in 1977 [73] which opens up planar graphs to divide-and-conquer.
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Planar graphs have many important applications in computer science, for example in VLSI layout. Many problems that are hard or even NP-complete for arbitrary graphs are much easier for planar graphs. In the next lecture we will prove a nice result due to Lipton and Tarjan in 1977 [73] which opens up planar graphs to divide-and-conquer.
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On 3-colorings of Plane Graphs
Acta Mathematicae Applicatae Sinica, English Series, 2004The main result of the paper states that any \(3\)-colouring of the vertices of a face of degree at least \(11\) in a planar graph \(G\) without cycles of length \(4\), \(5\) and \(7\) and with no pair of intersecting triangles (i.e. every two 3-cycles of \(G\) are vertex-disjoint) can be extended to a \(3\)-colouring of the whole graph \(G\).
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Eulerian partial duals of plane graphs
Journal of Graph Theory, 2018Metrose Metsidik, Xian'an Jin
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A note on 3-choosability of plane graphs under distance restrictions
Discret. Math. Algorithms Appl., 2017Jing Jin, Yiming Wei
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An improved bound on 2-distance coloring plane graphs with girth 5
Journal of combinatorial optimization, 2016Wei-Quan Dong, Wensong Lin
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Haplotype-resolved de novo assembly using phased assembly graphs with hifiasm
Nature Methods, 2021Haoyu Cheng +2 more
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Multiplex de Bruijn graphs enable genome assembly from long, high-fidelity reads
Nature Biotechnology, 2022Anton Bankevich +2 more
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