Results 61 to 70 of about 4,256 (307)

Set colourings of graphs

Discrete Mathematics, 1979
AbstractAn r-set colouring of a graph G is an assignment of r distinct colours to each vertex of G so that the sets of colours assigned to adjacent vertices are disjoint. We denote by χ(r)(G) the minimum number of colours required to r-set colour G. The set-chromatic number of G, denoted by χ*(G), is defined byχ*(G)=infrχ(r)(G)r.Clearly 2⩽χ*(G)⩽χ(G).By
Béla Bollobás, Andrew Thomason 0001
openaire   +2 more sources

Graph colouring algorithms [Elektronisk resurs] [PDF]

, 2015
This chapter presents an introduction to graph colouring algorithms. The focus is on vertex-colouring algorithms that work for general classes of graphs with worst-case performance guarantees in a sequential model of computation. The presentation aims to
Husfeldt, Thore,, Lund University.
core  

EDNRB‐dependent endothelin signaling reduces proliferation and promotes proneural‐to‐mesenchymal transition in gliomas

Molecular Oncology, EarlyView.
Glioma cells mainly express the endothelin receptor EDNRB, while EDNRA is restricted to a perivascular tumor subpopulation. Endothelin signaling reduces glioma cell proliferation while promoting migration and a proneural‐to‐mesenchymal transition associated with poor prognosis. This pathway activates Ca2+, K+, ERK, and STAT3 signalings and is regulated
Donovan Pineau, Leonor Garcia, Hugo Arnold, Antonija Hanžek, Maialen Arrieta, Laurent R Gauthier, Christine Granotier‐Beckers, François D Boussin, Amaury Herbet, Marie Hautière, Valentin Asei‐Ceschino, Clémentin Jacques, Laura Brard, Thomas Harnois, Valérie Coronas, Bruno Constantin, Aurélien Chatelier, Jean Chemin, Serge Urbach, Martial Seveno, Szimonetta Hideg, Chantal Ripoll, Kasandra Aguilar‐Cázarez, Min Zheng, Guo‐Hao Huang, Sheng‐Qing Lv, Lei Zhang, Philippe Rondard, Laurent Prezeau, Jean‐Philippe Pin, Hugues Duffau, Luc Bauchet, Valérie Rigau, Franck Denat, Charles Truillet, Didier Boquet, Jean‐Philippe Hugnot   +36 more
wiley   +1 more source

An upper bound for the chromatic number of line graphs [PDF]

Discrete Mathematics & Theoretical Computer Science, 2005
It was conjectured by Reed [reed98conjecture] that for any graph $G$, the graph's chromatic number $χ (G)$ is bounded above by $\lceil Δ (G) +1 + ω (G) / 2\rceil$ , where $Δ (G)$ and $ω (G)$ are the maximum degree and clique number of $G$, respectively ...
Andrew D. King, Bruce A. Reed, Adrian R. Vetta   +2 more
doaj   +1 more source

Somatic mutational landscape in von Hippel–Lindau familial hemangioblastoma

Molecular Oncology, EarlyView.
The causes of central nervous system (CNS) hemangioblastoma in Von Hippel–Lindau (vHL) disease are unclear. We used Whole Exome Sequencing (WES) on familial hemangioblastoma to investigate events that underlie tumor development. Our findings suggest that VHL loss creates a permissive environment for tumor formation, while additional alterations ...
Maja Dembic, Anne Nørremølle, Lilian Bomme Ousager, Lars van Brakel Andersen, Marie Louise Mølgaard Binderup, Mads Thomassen   +5 more
wiley   +1 more source

A Note on the Thue Chromatic Number of Lexicographic Products of Graphs

Discussiones Mathematicae Graph Theory, 2018
A sequence is called non-repetitive if none of its subsequences forms a repetition (a sequence r1r2⋯r2n such that ri = rn+i for all 1 ≤ i ≤ n). Let G be a graph whose vertices are coloured.
Peterin Iztok, Schreyer Jens, Škrabul’áková Erika Fecková, Taranenko Andrej   +3 more
doaj   +1 more source

Adaptor protein CIN85 potentiates the motility of osteosarcoma cells via the Akt/mTOR and MMP2‐COL3A1 axis

Molecular Oncology, EarlyView.
CIN85 is highly expressed in osteosarcoma, particularly in metastatic lesions. Its overexpression increases cell migration and Matrigel invasion, while silencing CIN85 suppresses these behaviors. Transcriptome analysis shows that CIN85 regulates MMP2, COL3A1, and Akt/mTOR signaling. Targeting these pathways reverses CIN85‐induced motility, highlighting
Iryna Horak, Iva Staniczková Zambo, Matěj Přikryl, Peter Múdry, Danica Zapletalová, Jarmila Navrátilová, Jiří Navrátil, Jan Šmarda, Liudmyla Drobot, Petr Beneš, Lucia Knopfová   +10 more
wiley   +1 more source

Notes on Nonrepetitive Graph Colouring [PDF]

The Electronic Journal of Combinatorics, 2008
A vertex colouring of a graph is nonrepetitive on paths if there is no path $v_1,v_2,\dots,v_{2t}$ such that $v_i$ and $v_{t+i}$ receive the same colour for all $i=1,2,\dots,t$. We determine the maximum density of a graph that admits a $k$-colouring that is nonrepetitive on paths.
János Barát, David R. Wood
openaire   +4 more sources

A PROCEDURE FOR DERIVING ODD-GRACEFUL CHROMATIC NUMBERS OF GRAPHS

Ural Mathematical Journal
Let \(G:=(V,E)\) be an undirected finite simple graph with vertex set \(V\) and edge set \(E\). A function \(c:V(G)\rightarrow \{1,2,\ldots,k\},\) for some positive integer \(k\), such that \(c(u)\neq c(v)\) for every edge \(uv\in E(G)\), is called a ...
I Nengah Suparta, I Gede Adhitya Wisnu Wardhana, I Gede Aris Gunadi, I Dewa Made Agus Ariawan   +3 more
doaj   +1 more source

Ordered colourings of graphs

Journal of Combinatorial Theory, Series B, 1982
An ordered colouring of a graph with k colours is a vertex colouring with colours {1, 2,…,k} such that each vertex coloured j is joined to at least one vertex-of colour i for each i less than j. Examples of ordered colourings are those produced by the greedy colouring algorithm.
Ernest J. Cockayne, Andrew G. Thomason
openaire   +2 more sources