Results 41 to 50 of about 892,665 (298)
On Aligned Bar 1-Visibility Graphs
Journal of Graph Algorithms and Applications, 2017 A graph is called a bar 1-visibility graph if its vertices can be represented as horizontal segments, called bars, and each edge corresponds to a vertical line of sight which can traverse another bar.
Franz Brandenburg +2 more
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Discussiones Mathematicae Graph Theory, 2023 DP-coloring is generalized via relaxed coloring and variable degeneracy in [P. Sittitrai and K. Nakprasit, Su cient conditions on planar graphs to have a relaxed DP-3-coloring, Graphs Combin. 35 (2019) 837–845], [K.M. Nakprasit and K.
Sribunhung Sarawute +3 more
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On planar hypohamiltonian graphs
Journal of Graph Theory, 2010 Summary: We present a planar hypohamiltonian graph on 42 vertices and (as a corollary) a planar hypotraceable graph on 162 vertices, improving the bounds of Zamfirescu and Zamfirescu and show some other consequences. We also settle the open problem whether there exists a positive integer \(N\), such that for every integer \(n\geq N\) there exists a ...
Wiener, Gabor, Araya, Makoto
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Planar and poly-arc Lombardi drawings
Journal of Computational Geometry, 2018 In Lombardi drawings of graphs, edges are represented as circular arcs and the edges incident on vertices have perfect angular resolution. It is known that not every planar graph has a planar Lombardi drawing.
Christian A. Duncan +5 more
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Planar Transitive Graphs [PDF]
The Electronic Journal of Combinatorics, 2018 We prove that the first homology group of every planar locally finite transitive graph $G$ is finitely generated as an $\Aut(G)$-module and we prove a similar result for the fundamental group of locally finite planar Cayley graphs. Corollaries of these results include Droms's theorem that planar groups are finitely presented and Dunwoody's theorem that
openaire +3 more sources
On Pathos Semitotal and Total Block Graph of a Tree [PDF]
, 2011 The concept of pathos of a graph G was introduced by Harary [2], as a collection of minimum number of line disjoint open paths whose union is G. The path number of a graph G is the number of paths in pathos.
Muddebihal M. H.
core +1 more source
3-degenerate induced subgraph of a planar graph [PDF]
, 2021 A graph $G$ is $d$-degenerate if every non-null subgraph of $G$ has a vertex of degree at most $d$. We prove that every $n$-vertex planar graph has a $3$-degenerate induced subgraph of order at least $3n/4$.Comment: 28 pages, 12 ...
Oum, Sang-il +12 more
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On certain prime cordial families of graphs
Journal of Taibah University for Science, 2020 Graph labelling is an important tool in modelling real life problems. In the present paper, different graph families are studied for prime cordial labelling.
Nazeran Idrees +3 more
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Quasipolynomiality of the Smallest Missing Induced Subgraph
Journal of Graph Algorithms and Applications, 2023 We study the problem of finding the smallest graph that does not occur as an induced subgraph of a given graph. This missing induced subgraph has at most logarithmic size and can be found by a brute-force search, in an $n$-vertex graph, in time $n^{O ...
David Eppstein +2 more
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Molecular Oncology, EarlyView.Tumour heterogeneity and clonal evolution of metastatic salivary gland cancer were evaluated in two patients with adenoid carcinoma and one patient with myoepithelial carcinoma. Radiology‐guided autopsy enabled multi‐region sampling (total samples n = 149), followed by whole‐genome sequencing and phylogenetic reconstruction (17 tumour samples, 4–7 per ...
Gerben Lassche +10 more
wiley +1 more source