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Outerplanar graph drawings with few slopes [PDF]
Computational geometry, 2014 We consider straight-line outerplanar drawings of outerplanar graphs in which a small number of distinct edge slopes are used, that is, the segments representing edges are parallel to a small number of directions.
Bartosz Walczak +16 more
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Bipolar fuzzy outerplanar graphs approach in image shrinking. [PDF]
Sci RepBipolar fuzzy outerplanar graphs are interesting and significant subclasses within the broader field of fuzzy graph theory. In this paper, bipolar fuzzy outerplanar graphs, and its properties are introduced.
Jaisankar D +3 more
europepmc +2 more sources
Planar, Outerplanar, and Toroidal Graphs of the Generalized Zero-Divisor Graph of Commutative Rings
Journal of mathematics, 2021 Let A be a commutative ring with unity and let set of all zero divisors of A ...
A. Alanazi, M. Nazim, N. ur Rehman
semanticscholar +1 more source
Large Induced Acyclic and Outerplanar Subgraphs of 2-Outerplanar Graph [PDF]
Graphs and Combinatorics, 2017 Albertson and Berman conjectured that every planar graph has an induced forest on half of its vertices. The best known lower bound, due to Borodin, is that every planar graph has an induced forest on two fifths of its vertices.
G. Borradaile +2 more
semanticscholar +1 more source
Algorithms for Outerplanar Graph Roots and Graph Roots of Pathwidth at Most 2 [PDF]
Algorithmica, 2017 Deciding if a graph has a square root is a classical problem, which has been studied extensively both from graph-theoretic and algorithmic perspective. As the problem is NP-complete, substantial effort has been dedicated to determining the complexity of ...
P. Golovach +4 more
semanticscholar +1 more source
On the maximum second eigenvalue of outerplanar graphs [PDF]
Discrete Mathematics, 2023 For a fixed positive integer $k$ and a graph $G$, let $\lambda_k(G)$ denote the $k$-th largest eigenvalue of the adjacency matrix of $G$. In 2017, Tait and Tobin proved that the maximum $\lambda_1(G)$ among all outerplanar graphs on $n$ vertices is ...
George Brooks +4 more
semanticscholar +1 more source
Shortest Beer Path Queries based on Graph Decomposition [PDF]
International Symposium on Algorithms and Computation, 2023 Given a directed edge-weighted graph $G=(V, E)$ with beer vertices $B\subseteq V$, a beer path between two vertices $u$ and $v$ is a path between $u$ and $v$ that visits at least one beer vertex in $B$, and the beer distance between two vertices is the ...
T. Hanaka +3 more
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On the Maximum Spread of Planar and Outerplanar Graphs [PDF]
Electronic Journal of Combinatorics, 2022 The spread of a graph $G$ is the difference between the largest and smallest eigenvalue of the adjacency matrix of $G$. Gotshall, O'Brien and Tait conjectured that for sufficiently large $n$, the $n$-vertex outerplanar graph with maximum spread is the ...
Zelong Li +3 more
semanticscholar +1 more source
Directed Acyclic Outerplanar Graphs Have Constant Stack Number [PDF]
IEEE Annual Symposium on Foundations of Computer Science, 2022 The stack number of a directed acyclic graph G is the minimum k for which there is a topological ordering of G and a k-coloring of the edges such that no two edges of the same color cross, i.e., have alternating endpoints along the topological ordering ...
Paul Jungeblut +2 more
semanticscholar +1 more source
Clique-Relaxed Graph Coloring [PDF]
, 2011 We define a generalization of the chromatic number of a graph G called the k-clique-relaxed chromatic number, denoted χ(k)(G). We prove bounds on χ(k)(G) for all graphs G, including corollaries for outerplanar and planar graphs.
Dunn, Charles +5 more
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