Results 21 to 30 of about 6,056 (148)
Improved bound for improper colourings of graphs with no odd clique minor
Combinatorics, Probability and Computing, 2022 AbstractStrengthening Hadwiger’s conjecture, Gerards and Seymour conjectured in 1995 that every graph with no odd $K_t$ -minor is properly $(t-1)$ -colourable. This is known as the Odd Hadwiger’s conjecture. We prove a relaxation of the above conjecture, namely we show that every graph with no odd $K_t$ -minor admits a vertex $(2t-2)$ -colouring ...
openaire +2 more sources
A Vertex-Splitting Lemma, de Werra's Theorem, and Improper List Colourings
Journal of Combinatorial Theory, Series B, 1998 AbstractWe prove a new vertex-splitting lemma which states that if a multigraphGhas maximum multiplicity of at mostp, then each vertex u can be split into ⌈(d(u)/p)⌉ new vertices, ⌊(d(u)/p)⌋ of degreep, with the multiple edges being shared out between the new vertices in such a way that each multiple edge remains intact at at least one of its two ...
Anthony J. W. Hilton +2 more
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Defective and Clustered Choosability of Sparse Graphs
, 2019 An (improper) graph colouring has "defect" $d$ if each monochromatic subgraph has maximum degree at most $d$, and has "clustering" $c$ if each monochromatic component has at most $c$ vertices.
Hendrey, Kevin, Wood, David R.
core +1 more source
The topological pigeonhole principle for ordinals [PDF]
, 2016 Given a cardinal $\kappa$ and a sequence $\left(\alpha_i\right)_{i\in\kappa}$ of ordinals, we determine the least ordinal $\beta$ (when one exists) such that the topological partition relation \[\beta\rightarrow\left(top\,\alpha_i\right)^1_{i\in\kappa}\]
Hilton, Jacob
core +3 more sources
Layout of Graphs with Bounded Tree-Width
, 2004 A \emph{queue layout} of a graph consists of a total order of the vertices, and a partition of the edges into \emph{queues}, such that no two edges in the same queue are nested. The minimum number of queues in a queue layout of a graph is its \emph{queue-
Albertson Michael +10 more
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Was Sierpinski right? III Can continuum--c.c. times c.c.c. be continuum--c.c.? [PDF]
, 1995 We prove the consistency of: if B_1, B_2 are Boolean algebra satisfying the c.c.c. and the 2^{aleph_0}-c.c.
Shelah, Saharon
core +3 more sources
Defective Coloring on Classes of Perfect Graphs
, 2020 In Defective Coloring we are given a graph $G$ and two integers $\chi_d$, $\Delta^*$ and are asked if we can $\chi_d$-color $G$ so that the maximum degree induced by any color class is at most $\Delta^*$.
Belmonte, Rémy +2 more
core +1 more source
Markov chain sampling of the $O(n)$ loop models on the infinite plane [PDF]
, 2017 It was recently proposed in https://journals.aps.org/pre/abstract/10.1103/PhysRevE.94.043322 [Herdeiro & Doyon Phys.,Rev.,E (2016)] a numerical method showing a precise sampling of the infinite plane 2d critical Ising model for finite lattice subsections.
Herdeiro, Victor
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Risk analysis of the Unity 1.5T MR‐Linac adapt‐to‐shape workflow
Journal of Applied Clinical Medical Physics, EarlyView.Abstract Background and Purpose The adapt‐to‐shape (ATS) workflow on the Unity MR‐Linac (Elekta AB, Stockholm, Sweden) allows for full replanning including recontouring and reoptimization5. Additional complexity to this workflow is added when the adaptation involves the use of MIM Maestro (MIM Software, Cleveland, OH) software in conjunction with ...
Jiayi Liang +13 more
wiley +1 more source
Advanced Engineering Materials, EarlyView.Hydrostatic bearings excel in high‐precision applications, but their performance hinges on a continuous external supply. This study evaluates various material combinations for sliding surfaces to mitigate damage during supply failures or misalignment and to discover the most effective materials identified for enhancing the reliability and efficiency of
Michal Michalec +6 more
wiley +1 more source