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Exact Bounds for Distributed Graph Colouring [PDF]
Colloquium on Structural Information & Communication Complexity, 2015 We prove exact bounds on the time complexity of distributed graph colouring. If we are given a directed path that is properly coloured with n colours, by prior work it is known that we can find a proper 3-colouring in $\frac{1}{2} \log^{*}n \pm O1 ...
Joel Rybicki, J. Suomela
semanticscholar +1 more source
Connected greedy colourings of perfect graphs and other classes: the good, the bad and the ugly [PDF]
Discrete Mathematics & Theoretical Computer ScienceThe Grundy number of a graph is the maximum number of colours used by the "First-Fit" greedy colouring algorithm over all vertex orderings. Given a vertex ordering $\sigma= v_1,\dots,v_n$, the "First-Fit" greedy colouring algorithm ...
Laurent Beaudou +6 more
doaj +1 more source
Bilangan Kromatik Grap Commuting dan Non Commuting Grup Dihedral
Cauchy: Jurnal Matematika Murni dan Aplikasi, 2015 Commuting graph is a graph that has a set of points X and two different vertices to be connected directly if each commutative in G. Let G non abelian group and Z(G) is a center of G.
Handrini Rahayuningtyas +2 more
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List circular backbone colouring [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 A natural generalization of graph colouring involves taking colours from a metric space and insisting that the endpoints of an edge receive colours separated by a minimum distance dictated by properties of the edge.
Frederic Havet, Andrew D. King
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Bounds On Fuzzy Dominator Chromatic Number of Fuzzy Soft Bipartite Graphs
Ratio Mathematica, 2023 An FSG GS(T,V) fuzzy’s soft dominator colouring (FSDC) is a suitable Fuzzy Soft Colouring (FSC) where every node of a colour group is dominated by a vertex of GS(T,V).
Jahir Hussain R, Afya Farhana M
doaj +1 more source
Delay Colouring in Quartic Graphs [PDF]
The Electronic Journal of Combinatorics, 2020 Haxell, Wilfong, and Winkler conjectured that every bipartite graph with maximum degree $\Delta$ is $(\Delta + 1)$-delay-colourable. We prove this conjecture in the special case $\Delta = 4$.
Edwards, Katherine, Kennedy, W. Sean
openaire +1 more source
The Balanced Decomposition Number of TK4 and Series-Parallel Graphs
Discussiones Mathematicae Graph Theory, 2013 A balanced colouring of a graph G is a colouring of some of the vertices of G with two colours, say red and blue, such that there is the same number of vertices in each colour. The balanced decomposition number f(G) of G is the minimum integer s with the
Fujita Shinya, Liu Henry
doaj +1 more source
Molecular Oncology, EarlyView.In this exploratory study, we investigated the relationship between the gut microbiota and outcome in patients with metastatic hormone receptor‐positive breast cancer, treated in a randomized clinical trial with chemotherapy alone or chemotherapy in combination with immune checkpoint blockade.
Andreas Ullern +7 more
wiley +1 more source
Graph Colouring as a Challenge Problem for Dynamic Graph Processing on Distributed Systems
International Conference for High Performance Computing, Networking, Storage and Analysis, 2016 An unprecedented growth in data generation is taking place. Data about larger dynamic systems is being accumulated, capturing finer granularity events, and thus processing requirements are increasingly approaching real-time.
Scott Sallinen +5 more
semanticscholar +1 more source
Molecular Oncology, EarlyView.Following high dose rate brachytherapy (HDR‐BT) for hepatocellular carcinoma (HCC), patients were classified as responders and nonresponders. Post‐therapy serum induced increased BrdU incorporation and Cyclin E expression of Huh7 and HepG2 cells in nonresponders, but decreased levels in responders.
Lukas Salvermoser +14 more
wiley +1 more source