Results 71 to 80 of about 2,715,030 (252)

Bipartite graphs and quasipositive surfaces [PDF]

, 2013
We present a simple combinatorial model for quasipositive surfaces and positive braids, based on embedded bipartite graphs. As a first application, we extend the well-known duality on standard diagrams of torus links to twisted torus links.
SEBASTIAN BAADER, Baader, Sebastian
core   +2 more sources

Explicit 3‐colorings for Exponential Graphs

Journal 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, Pierre Charbit, Alantha Newman   +2 more
wiley   +1 more source

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

Algorithm and Hardness Results for Outer-connected Dominating Set in Graphs

Journal of Graph Algorithms and Applications, 2014
A set D ⊆ V of a graph G = (V,E) is called an outer-connected dominating set of G if for all v ∈ V, |NG[v]∩D| ≥ 1, and the induced subgraph of G on V\D is connected.
B. Panda, Arti Pandey
doaj   +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

Efficient Generation of Different Topological Representations of Graphs Beyond-Planarity

Journal of Graph Algorithms and Applications, 2020
Beyond-planarity focuses on combinatorial properties of classes of non-planar graphs that allow for representations satisfying certain local geometric or topological constraints on their edge crossings.
Patrizio Angelini, Michael Bekos, Michael Kaufmann, Thomas Schneck   +3 more
doaj   +1 more source

Independent Complementary Distance Pattern Uniform Graphs [PDF]

, 2009
A graph G =(V,E) is called to be Smarandachely uniform k-graph for an integer k ≥ 1ifthereexistsM1,M2, ·· ·,Mk ⊂ V (G) such that fMi (u) ={d(u, v):v ∈ Mi} for ∀u ∈ V (G)−Mi is independent of the choice of u ∈ V (G)−Mi and integer i, 1 ≤ i ≤ k.
Koshy, Beena, Germina K.A., Germina K. A., Beena Koshy   +3 more
core   +1 more source

Characterization of Graphs Without Even F $F$‐Orientations

Journal of Graph Theory, EarlyView.
ABSTRACT A graph G $G$ is 1‐extendable if every edge belongs to at least one 1‐factor of G $G$. Let G $G$ be a graph with a 1‐factor F $F$. Then an even (odd) F $F$ ‐orientation of G $G$ is an orientation in which each F $F$‐alternating cycle has exactly an even (odd) number of edges directed in the same fixed direction around the cycle.
Marién Abreu, Domenico Labbate, Federico Romaniello, John Sheehan   +3 more
wiley   +1 more source

On Graphs Which Have Locally Complete 2‐Edge‐colourings and Their Relationship to Proper Circular‐Arc Graphs

Journal of Graph Theory, EarlyView.
ABSTRACT A 2‐edge‐coloured graph G $G$ is called locally complete if for each vertex v $v$, the vertices adjacent to v $v$ through edges of the same colour induce a complete subgraph in G $G$. Locally complete 2‐edge‐coloured graphs have nice properties, and there exists a polynomial algorithm to decide whether such a graph has an alternating ...
Jørgen Bang‐Jensen, Jing Huang
wiley   +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