Results 181 to 190 of about 886,125 (210)

On list‐coloring outerplanar graphs

Journal of Graph Theory, 2008
AbstractWe prove that a 2‐connected, outerplanar bipartite graph (respectively, outerplanar near‐triangulation) with a list of colors L (v ) for each vertex v such that $|L(v)|\geq\min\{{\deg}(v),4\}$ (resp., $|L(v)|\geq{\min}\{{\deg}(v),5\}$) can be L‐list‐colored (except when the graph is K3 with identical 2‐lists).
openaire   +2 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

A characterization of ?-outerplanar graphs

Journal of Graph Theory, 1996
Chartrand and Harary have shown that if G is a non-outerplanar graph such that, for every edge e, both the deletion G\e and the contraction G/e of e from G are outerplanar, then G is isomorphic to K4 or K2,3. An α-outerplanar graph is a graph which is not outerplanar such that, for some edge α, both G\α and G/α are outerplanar.
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Independent domination in outerplanar graphs

Discrete Applied Mathematics, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Goddard, Wayne, Henning, Michael A.
openaire   +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

Embedding Outerplanar Graphs in Small Books

SIAM Journal on Algebraic Discrete Methods, 1987
A book consists of a number of half-planes (pages) sharing a common boundary line (the spine). A book embedding of a graph embeds the vertices on the spine and each edge in some page so that each page contains a plane subgraph. The width of a page is the maximum number of edges that intersect any half-line perpendicular to the spine in the page.
openaire   +1 more source

Internally-Convex Drawings of Outerplanar Graphs in Small Area

International Symposium Graph Drawing and Network Visualization
A well-known result by Kant [Algorithmica, 1996] implies that n-vertex outerplane graphs admit embedding-preserving planar straight-line grid drawings where the internal faces are convex polygons in $O(n^2)$ area.
M. Bekos, G. D. Lozzo, Fabrizio Frati, G. Liotta, A. Symvonis   +4 more
semanticscholar   +1 more source

Augmenting the Connectivity of Outerplanar Graphs

Algorithmica, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
García, A., Hurtado, F., Noy, M., Tejel, J.   +3 more
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Secure Total Domination Number in Maximal Outerplanar Graphs

Discrete Applied Mathematics
A subset $S$ of vertices in a graph $G$ is a secure total dominating set of $G$ if $S$ is a total dominating set of $G$ and, for each vertex $u \not\in S$, there is a vertex $v \in S$ such that $uv$ is an edge and $(S \setminus \{v\}) \cup \{u\}$ is also
Yasufumi Aita, Toru Araki
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