Results 201 to 210 of about 850,474 (224)

Augmenting Outerplanar Graphs

Journal of Algorithms, 1996
Summary: We show that for outerplanar graphs \(G\) the problem of augmenting \(G\) by adding a minimum number of edges such that the augmented graph \(G'\) is planar and bridge-connected, biconnected, or triconnected can be solved in linear time and space.
openaire   +4 more sources

An algorithm for outerplanar graphs with parameter

Journal of Algorithms, 1991
Summary: For \(n\)-vertex outerplanar graphs, it is proven that \(O(n^{2.87})\) is an upper bound on the number of breakpoints of the function which gives the maximum weight of an independent set, where the vertex weights vary as linear functions of a parameter. An \(O(n^{2.87})\) algorithm for finding the solution is proposed.
Binghuan Zhu, Wayne Goddard
openaire   +3 more sources

A characterization of ?-outerplanar graphs

Journal of Graph Theory, 1996
The graphs investigated in this paper can have loops and parallel edges. An outerplanar graph is a graph that has a planar embedding in which all its vertices lie on the boundary of the infinite face. And an \(\alpha\)-outerplanar graph is a graph \(G\) which is not outerplanar such that, for some edge \(\alpha\), both the deletion \(G\backslash \alpha\
openaire   +3 more sources

Odd 4-Coloring of Outerplanar Graphs

Graphs Comb.
A proper $k$-coloring of $G$ is called an odd coloring of $G$ if for every vertex $v$, there is a color that appears at an odd number of neighbors of $v$.
Masaki Kashima, Xuding Zhu
semanticscholar   +1 more source

Bounds on the Fibonacci Number of a Maximal Outerplanar Graph

The Fibonacci quarterly, 1998
All graphs in this article are finite, undirected, without loops or multiple edges. Let G be a graph with vertices vl5 v2,..., vn. The complement in G of a subgraph H is the subgraph of G obtained by deleting all edges in H.
A. F. Alameddine
semanticscholar   +1 more source

Large Induced Subgraphs of Bounded Degree in Outerplanar and Planar Graphs

arXiv.org
In this paper, we study the following question. Let $\mathcal G$ be a family of planar graphs and let $k\geq 3$ be an integer. What is the largest value $f_k(n)$ such that every $n$-vertex graph in $\mathcal G$ has an induced subgraph with degree at most
Marco D'Elia, Fabrizio Frati
semanticscholar   +1 more source

Bottleneck matrices of maximal outerplanar graphs with isomorphic underlying trees

Linear and multilinear algebra
In this paper, we consider the entries of the bottleneck matrices of maximal outerplanar graphs with isomorphic underlying trees. We show how the entries of the bottleneck matrix are perturbed when we modify a maximal outerplanar graph into a ...
Jason J. Molitierno
semanticscholar   +1 more source

From Planar via Outerplanar to Outerpath - Engineering NP-Hardness Constructions (Poster Abstract)

International Symposium Graph Drawing and Network Visualization
A typical question in graph drawing is to determine, for a given graph drawing style, the boundary between polynomial-time solvability and NP -hardness. For two examples from the area of drawing graphs with few slopes, we sharpen this boundary.
Joshua Geis, Johannes Zink
semanticscholar   +1 more source

Centers of maximal outerplanar graphs

Journal of Graph Theory, 1980
AbstractThe center of a graph is defined to be the subgraph induced by the set of vertices that have minimum eccentricities (i.e., minimum distance to the most distant vertices). It is shown that only seven graphs can be centers of maximal outerplanar graphs.
openaire   +3 more sources

Large induced subgraph with a given pathwidth in outerplanar graphs

arXiv.org
A long-standing conjecture by Albertson and Berman states that every planar graph of order $n$ has an induced forest with at least $\lceil \frac{n}{2} \rceil$ vertices.
Naoki Matsumoto, Takamasa Yashima
semanticscholar   +1 more source