Results 171 to 180 of about 2,913 (200)

Saturated Partial Embeddings of Planar Graphs

Journal of Graph Theory, EarlyView.
ABSTRACT In this work, we study how far one can deviate from optimal behavior when embedding a planar graph. For a planar graph G $G$, we say that a plane subgraph H ⊆ G $H\subseteq G$ is a plane‐saturated subgraph if adding any edge (possibly with new vertices) to H $H$ would either violate planarity or make the resulting graph no longer a subgraph of
Alexander Clifton, Nika Salia
wiley   +1 more source

One-shot distillation with constant overhead using catalysts. [PDF]

Nat Commun
Fang K, Liu ZW.
europepmc   +1 more source

A Note on Lovász Characterization of Perfect Graphs

Journal of Graph Theory, EarlyView.
ABSTRACT A graph is perfect if, for every induced subgraph, the chromatic number equals the size of its largest clique. In 1972, Lovász established a fundamental characterization of perfect graphs, showing that a graph is perfect if and only if, for every induced subgraph, the product of the size of the largest independent set and the size of the ...
James Alex
wiley   +1 more source

Identity-by-descent segments in large samples. [PDF]

Theor Popul Biol
Temple SD, Thompson EA.
europepmc   +1 more source

The 1 3 $\frac{1}{3}$‐Conjectures for Domination in Cubic Graphs

Journal of Graph Theory, EarlyView.
ABSTRACT A set S $S$ of vertices in a graph G $G$ is a dominating set of G $G$ if every vertex not in S $S$ is adjacent to a vertex in S $S$. The domination number of G $G$, denoted by γ ( G ) $\gamma (G)$, is the minimum cardinality among all dominating sets in G $G$. In a breakthrough paper in 2008, Löwenstein and Rautenbach proved that if G $G$ is a
Paul Dorbec, Michael A. Henning
wiley   +1 more source

Flow‐Critical Graphs

Journal of Graph Theory, EarlyView.
ABSTRACT Lovász et al. proved that every six‐edge‐connected graph has a nowhere‐zero three‐flow. In fact, they proved a more technical statement, which says that there exists a nowhere‐zero three‐flow that extends the flow prescribed on the incident edges of a single vertex z $z$ with bounded degree. We extend this theorem of Lovász et al.
Arnbjörg Soffía Árnadóttir, Zdeněk Dvořák, Bernard Lidický, Benjamin Moore, Evelyne Smith‐Roberge, Robert Šámal   +5 more
wiley   +1 more source

Qualitative analysis and numerical simulation of ABC fractional impulsive differential systems with implicit nonlinear terms and integral boundary conditions. [PDF]

PLoS One
Sharif AA, Hamood M, Ghadle KP.
europepmc   +1 more source

From Finding a Spanning Subgraph H $H$ to an H $H$‐Factor

Journal of Graph Theory, EarlyView.
ABSTRACT A typical Dirac‐type problem in extremal graph theory is to determine the minimum degree threshold for a graph G $G$ to have a spanning subgraph H $H$, for example, the Dirac theorem. A natural follow‐up problem is to seek an H $H$‐factor, which is a spanning set of vertex‐disjoint copies of H $H$.
Allan Lo
wiley   +1 more source

Stability and Hopf bifurcation analysis of a fractional-order Filippov prey-predator model with prey refuge and fear effects. [PDF]

Sci Rep
Nadeem M, Ramesh P, Sambath M, Alsayaad Y.   +3 more
europepmc   +1 more source

A Structural Description of Zykov and Blanche Descartes Graphs

Journal of Graph Theory, EarlyView.
ABSTRACT Around 1950, Zykov and Blanche Descartes proposed the two first explicit constructions of triangle‐free graphs with arbitrarily large chromatic number. We define a Zykov (resp. Blanche Descartes) graph as any induced subgraph of a graph created using Zykov's construction (resp. Blanche Descartes's).
Malory Marin, Stéphan Thomassé, Nicolas Trotignon, Rémi Watrigant   +3 more
wiley   +1 more source