Results 141 to 150 of about 4,847 (217)

Explicit 3‐colorings for Exponential Graphs

open access: yesJournal of Graph Theory, EarlyView.
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

Flexible List Coloring of Graphs With Maximum Average Degree Less Than 3

open access: yesJournal of Graph Theory, EarlyView.
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

Path Degeneracy and Applications

open access: yesJournal of Graph Theory, EarlyView.
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
wiley   +1 more source

Farming in the shadows of Rome: A multi‐proxy palaeoenvironmental record from Loch Clunie—Perthshire

open access: yesJournal of Quaternary Science, EarlyView.
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

Jewelled Byzantine and Medieval Reliquaries of the True Cross: Peridots and Other Gemstones in Material and Symbolic Perspective

open access: yesJournal of Raman Spectroscopy, EarlyView.
An interdisciplinary in situ study of jewelled reliquaries of the True Cross integrates gemmology and portable analytical techniques, revealing new evidence on the identification and symbolic role of peridots and other gemstones. ABSTRACT Jewelled crosses containing relics of the True Cross occupy a central position in the devotional, artistic and ...
Stefania Martiniello   +2 more
wiley   +1 more source

Home - About - Disclaimer - Privacy