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A survey on book-embedding of planar graphs
The book-embedding problem arises in several area, such as very large scale integration (VLSI) design and routing multilayer printed circuit boards...
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Planar Graphs
In Graph Theory, a planar graph is a graph which can be embedded in the plane i.e., it can be drawn on the plane in such a manner that its edges...
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Planar Graphs
In Graph Theory, a planar graph is a graph which can be embedded in the plane i.e., it can be drawn on the plane in such a manner that its edges...
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Universal Planar Graphs for the Topological Minor Relation
Huynh et al. recently showed that a countable graph G which contains every countable planar graph as a subgraph must contain arbitrarily large finite...
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Domination in Planar Graphs
In this chapter, we present results on the core domination parameters in planar graphs. We shall adopt the following terminology for planar graphs. A...
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Dynamic Compact Planar Embeddings
This paper presents a way to compactly represent dynamic connected planar embeddings, which may contain self loops and multi-edges, in...
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On the oriented diameter of planar triangulations
The diameter of an undirected or a directed graph is defined to be the maximum shortest path distance over all pairs of vertices in the graph. Given...
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A Note on 3-Distance Coloring of Planar Graphs
Thomassen (J. Combin. Theory Ser B 128:192–218, 2018) showed that every subcubic planar graph has 2-distance chromatic number at most 7, which was...
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Embedding Dimensions of Simplicial Complexes on Few Vertices
We provide a simple characterization of simplicial complexes on few vertices that embed into the d -sphere. Namely, a simplicial complex on
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Kasteleyn cokernels and perfect matchings on planar bipartite graphs
The determinant method of Kasteleyn gives a method of computing the number of perfect matchings of a planar bipartite graph. In addition, results of...
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Embedding Grid Graphs on Surfaces
In this paper, we analyze embeddings of grid graphs on orientable surfaces. We determine the genus of two infinite classes of 3-dimensional grid...
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A Time-Continuous Embedding Method for Scalar Hyperbolic Conservation Laws on Manifolds
A time-continuous (tc-)embedding method is first proposed for solving nonlinear scalar hyperbolic conservation laws with discontinuous solutions...
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Weak Dynamic Coloring of Planar Graphs
The k - weak-dynamic number of a graph G is the smallest number of colors we need to color the vertices of G in such a way that each vertex v of degree d (...
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The Sandpile Group of a Trinity and a Canonical Definition for the Planar Bernardi Action
Baker and Wang define the so-called Bernardi action of the sandpile group of a ribbon graph on the set of its spanning trees. This potentially...
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Chords of 2-Factors in Planar Cubic Bridgeless Graphs
We show that every edge in a 2-edge-connected planar cubic graph is either contained in a 2-edge-cut or is a chord of some cycle contained in a...
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Linear-size formulations for connected planar graph partitioning and political districting
Motivated by applications in political districting, we consider the task of partitioning the n vertices of a planar graph into k connected...
