Results 11 to 20 of about 848,049 (294)

Splitting Plane Graphs to Outerplanarity

Journal of Graph Algorithms and Applications, 2023
Vertex splitting replaces a vertex by two copies and partitions its incident edges amongst the copies. This problem has been studied as a graph editing operation to achieve desired properties with as few splits as possible, most often planarity, for ...
Martin Gronemann, Martin Nöllenburg, Anaïs Villedieu   +2 more
doaj   +5 more sources

An algorithmic characterization and spectral analysis of canonical splitting signed graph ξ(Σ)

MethodsX
An ordered pair Σ=(Σu,σ) is called the signed graph, where Σu=(V,E) is an underlying graph and σ is a signed mapping, called signature, from E to the sign set {+,−}. A marking of Σ is a function μ:V(Σ)→{+,−}.
Deepa Sinha, Sandeep Kumar
doaj   +2 more sources

Planarizing graphs and their drawings by vertex splitting

Journal of Computational Geometry, 2023
The splitting number of a graph $G=(V,E)$ is the minimum number of vertex splits required to turn $G$ into a planar graph, where a vertex split removes a vertex $v \in V$, introduces two new copies $v_1$, $v_2$ of $v$, and distributes the edges formerly
Martin Nöllenburg, Manuel Sorge, Soeren Terziadis, Anaïs Villedieu, Hsiang-Yun Wu, Jules Wulms   +5 more
doaj   +6 more sources

On the split reliability of graphs

Networks, 2023
AbstractA common model of robustness of a graph against random failures has all vertices operational, but the edges independently operational with probability . One can ask for the probability that all vertices can communicate (all‐terminal reliability) or that two specific vertices (or terminals) can communicate with each other (two‐terminal ...
Jason I. Brown, Isaac McMullin
openaire   +2 more sources

Splitting an Expander Graph [PDF]

Journal of Algorithms, 1999
The authors consider partitions \(E = E_1 \cup E_2 \cup\cdots\cup E_k\) of the edge set of an \(r\)-regular expander graph \(G = (V,E)\) such that the graphs \(G_i = (V,E_i)\) are expanders. Certain algorithms for finding edge disjoint paths use such partitions. A nonconstructive proof using the Lovász local lemma shows that very good partitions exist.
Alan M. Frieze, Michael Molloy 0001
openaire   +3 more sources

Splitting Vertices in 2-Layer Graph Drawings

, 2023
Bipartite graphs model the relationships between two disjoint sets of entities in several applications and are naturally drawn as 2-layer graph drawings. In such drawings, the two sets of entities (vertices) are placed on two parallel lines (layers), and
Angelini, Patrizio, Kindermann, Philipp, Wallinger, Markus, Ahmed, Reyan, Di Battista, Giuseppe, Bekos, Michael A., Kaufmann, Michael, Symvonis, Antonios, Villedieu, Anaïs, Kobourov, Stephen, Nöllenburg, Martin   +10 more
core   +4 more sources

Power domination in splitting and degree splitting graph

, 2021
A vertex set S is called a power dominating set of a graph G if every vertex within the system is monitored by the set S following a collection of rules for power grid monitoring.
Anitha, Dr.J., Anitha, J., Muthukumar, S.   +2 more
core   +1 more source

Pebbling in Split Graphs [PDF]

SIAM Journal on Discrete Mathematics, 2014
Graph pebbling is a network optimization model for transporting discrete resources that are consumed in transit: the movement of 2 pebbles across an edge consumes one of the pebbles. The pebbling number of a graph is the fewest number of pebbles $t$ so that, from any initial configuration of $t$ pebbles on its vertices, one can place a pebble on any ...
Alcón, Liliana Graciela, Gutiérrez, Marisa, Hurlber, Glenn   +2 more
openaire   +6 more sources

Probe split graphs [PDF]

Discrete Mathematics & Theoretical Computer Science, 2007
Graphs and Algorithms An undirected graph G=(V,E) is a probe split graph if its vertex set can be partitioned into two sets, N (non-probes) and P (probes) where N is independent and there exists E' ⊆ N× N such that G'=(V,E∪ E') is a split graph. Recently Chang et al. gave an O(V4(V+E)) time recognition algorithm for probe split graphs.
Le, van Bang, Ridder, H. N.
openaire   +6 more sources

Detection, tracking and event localization of jet stream features in 4-D atmospheric data [PDF]

Geoscientific Model Development, 2012
We introduce a novel algorithm for the efficient detection and tracking of features in spatiotemporal atmospheric data, as well as for the precise localization of the occurring genesis, lysis, merging and splitting events.
S. Limbach, E. Schömer, H. Wernli
doaj   +1 more source