Results 51 to 60 of about 13,653 (313)
Rainbow Path and Color Degree in Edge Colored Graphs [PDF]
The Electronic Journal of Combinatorics, 2014 Let $G$ be an edge colored graph. A rainbow pathin $G$ is a path in which all the edges are colored with distinct colors. Let $d^c(v)$ be the color degree of a vertex $v$ in $G$, i.e. the number of distinct colors present on the edges incident on the vertex $v$. Let $t$ be the maximum length of a rainbow path in $G$.
Das, Anita +2 more
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Asymmetry in Hydrophobicity Induces Electric Potential in Non‐Charged Biomolecular Condensates
Advanced Science, EarlyView.Non‐charged biomolecular condensates can encode electric potential gradient through defining asymmetry in environmental hydrophobicity. ABSTRACT The capacity of biomolecular condensates to establish and modulate electrochemical equilibria is emerging as an important functioning mechanism in cellular biochemistry.
Leshan Yang +3 more
wiley +1 more source
MathematicsAn edge-coloring σ of a connected graph G is called rainbow if there exists a rainbow path connecting any pair of vertices. In contrast, σ is monochromatic if there is a monochromatic path between any two vertices.
Mohammed A. Mutar +2 more
doaj +1 more source
The rainbow 2-connectivity of Cartesian products of 2-connected graphs and paths
Electronic Journal of Graph Theory and Applications, 2020 An edge-colored graph G is rainbow k-connected, if there are k-internally disjoint rainbow paths connecting every pair of vertices of G. The rainbow k-connection number of G, denoted by rck(G), is the minimum number of colors needed for which there ...
Bety Hayat Susanti +2 more
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Bounded colorings of multipartite graphs and hypergraphs
, 2016 Let $c$ be an edge-coloring of the complete $n$-vertex graph $K_n$. The problem of finding properly colored and rainbow Hamilton cycles in $c$ was initiated in 1976 by Bollob\'as and Erd\H os and has been extensively studied since then.
Kamčev, Nina +2 more
core +1 more source
Deep Learning‐Assisted Coherent Raman Scattering Microscopy
Advanced Intelligent Discovery, EarlyView.The analytical capabilities of coherent Raman scattering microscopy are augmented through deep learning integration. This synergistic paradigm improves fundamental performance via denoising, deconvolution, and hyperspectral unmixing. Concurrently, it enhances downstream image analysis including subcellular localization, virtual staining, and clinical ...
Jianlin Liu +4 more
wiley +1 more source
Graphs with 3-rainbow index $n-1$ and $n-2$ [PDF]
, 2013 Let $G$ be a nontrivial connected graph with an edge-coloring $c:E(G)\rightarrow \{1,2,\ldots,q\},$ $q\in \mathbb{N}$, where adjacent edges may be colored the same. A tree $T$ in $G$ is a $rainbow tree$ if no two edges of $T$ receive the same color.
Li, Xueliang, Yang, Kang, Zhao, Yan
core
Improved Inapproximability of Rainbow Coloring [PDF]
, 2020 A rainbow $q$-coloring of a $k$-uniform hypergraph is a $q$-coloring of the vertex set such that every hyperedge contains all $q$ colors. We prove that given a rainbow $(k - 2\lfloor \sqrt{k}\rfloor)$-colorable $k$-uniform hypergraph, it is NP-hard to find a normal $2$-coloring.
Austrin, Per +2 more
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The Anatomical Record, EarlyView.Abstract Dinosaurs evolved a unique respiratory system with air sacs that contributed to their evolutionary success. Postcranial skeletal pneumaticity (PSP) has been used to infer the presence of air sac systems in some fossil archosaurs. While unambiguous evidence of PSP is well documented in pterosaurs and post‐Carnian saurischians, it remains absent
Tito Aureliano +3 more
wiley +1 more source
Discussiones Mathematicae Graph Theory, 2015 Given a coloring of the vertices, we say subgraph H is monochromatic if every vertex of H is assigned the same color, and rainbow if no pair of vertices of H are assigned the same color. Given a graph G and a graph F, we define an F-WORM coloring of G as
Goddard Wayne, Wash Kirsti, Xu Honghai
doaj +1 more source