Explicit 3‐colorings for Exponential Graphs
ABSTRACT In 1985, El‐Zahar and Sauer showed that the chromatic number of the direct product of two 4‐chromatic graphs is 4, establishing a nontrivial case of Hedetniemi's conjecture, which has since been refuted in general. Their proof uses the concept of an exponential graph, showing that if a graph H $H$ has no proper 3‐coloring, then the exponential
Adrien Argento +2 more
wiley +1 more source
DualStream-RTNet: A Multimodal Deep Learning Framework for Grape Cultivar Classification and Soluble Solid Content Prediction. [PDF]
Liu Z +7 more
europepmc +1 more source
Flexible List Coloring of Graphs With Maximum Average Degree Less Than 3
ABSTRACT In the flexible list coloring problem, we consider a graph G $G$ and a color list assignment L $L$ on G $G$, as well as a subset U ⊆ V ( G ) $U\subseteq V(G)$ for which each u ∈ U $u\in U$ has a preferred color p ( u ) ∈ L ( u ) $p(u)\in L(u)$. Our goal is to find a proper L $L$‐coloring ϕ $\phi $ of G $G$ such that ϕ ( u ) = p ( u ) $\phi (u)=
Richard Bi, Peter Bradshaw
wiley +1 more source
In vitro performance of violet LED and argon plasma with oxygen on dentin bleaching. [PDF]
Aidar KMS +8 more
europepmc +1 more source
Path Degeneracy and Applications
ABSTRACT In this work, we relate girth and path‐degeneracy in classes with sub‐exponential expansion, with explicit bounds for classes with polynomial expansion and proper minor‐closed classes that are tight up to a constant factor (and tight up to second order terms if a classical conjecture on existence of g $g$‐cages is verified). As an application,
Yuquan Lin, Patrice Ossona de Mendez
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Colors for Resources: Reward-Linked Visual Displays in Orchids. [PDF]
Coimbra G +4 more
europepmc +1 more source
On Sparsity Conditions Guaranteeing a Fractional Coloring
ABSTRACT A graph has an ( a : b ) $(a:b)$ ‐coloring if there exists an assignment from the vertices to subsets of { 1 , … , a } $\{1,\ldots ,a\}$ with size b $b$ such that adjacent vertices are assigned disjoint subsets. Odd girth at least 2 k + 1 $2k+1$ is a necessary condition for a graph to have a ( 2 k + 1 : k ) $(2k+1:k)$‐coloring.
Ilkyoo Choi
wiley +1 more source
Effect of Acidification on the Properties of Films Developed from Carboxymethylcellulose and Jabuticaba Anthocyanin Extract (<i>Plinia Cauliflora</i>). [PDF]
Ponciano CDS, de Oliveira CP.
europepmc +1 more source
Farming in the shadows of Rome: A multi‐proxy palaeoenvironmental record from Loch Clunie—Perthshire
ABSTRACT Roman impacts on local society is a subject of international significance. Loch Clunie, Perthshire, lies only 5.4 km from Inchtuthil, the only Roman legionary fortress in Scotland, and contains two crannogs and a probable lakeside hillfort. Despite this proximity and the likelihood of local–Roman interaction, these sites remain unexcavated ...
Samantha E. Jones +6 more
wiley +1 more source
Cognition does not automatically influence perception: Evidence from neural encoding of colors belonging to different categories. [PDF]
Martinovic J +5 more
europepmc +1 more source

