Results 41 to 50 of about 569,825 (280)
Edge Partitions of Optimal $2$-plane and $3$-plane Graphs
, 2018 A topological graph is a graph drawn in the plane. A topological graph is $k$-plane, $k>0$, if each edge is crossed at most $k$ times. We study the problem of partitioning the edges of a $k$-plane graph such that each partite set forms a graph with a ...
CSA Nash-Williams +12 more
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On Partitioning the Edges of 1-Plane Graphs
, 2016 A 1-plane graph is a graph embedded in the plane such that each edge is crossed at most once. A 1-plane graph is optimal if it has maximum edge density.
Lenhart, William J. +2 more
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Aequationes Mathematicae, 1975 The orthogonality relation among subspaces of a finite vector space is studied here by means of the corresponding graph. In the case we consider, this graph has some highly symmetric induced subgraphs. We find three infinite families of graphs of girth 3, and two infinite families of graphs of girth 5, whose automorphism groups are transitive on ...
openaire +2 more sources
L-Visibility Drawings of IC-planar Graphs
, 2015 An IC-plane graph is a topological graph where every edge is crossed at most once and no two crossed edges share a vertex. We show that every IC-plane graph has a visibility drawing where every vertex is an L-shape, and every edge is either a horizontal ...
AM Dean +6 more
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Bipartite partial duals and circuits in medial graphs
, 2012 It is well known that a plane graph is Eulerian if and only if its geometric dual is bipartite. We extend this result to partial duals of plane graphs. We then characterize all bipartite partial duals of a plane graph in terms of oriented circuits in its
A Asratian +18 more
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Every plane graph of maximum degree 8 has an edge-face 9-colouring [PDF]
, 2011 An edge-face colouring of a plane graph with edge set $E$ and face set $F$ is a colouring of the elements of $E \cup F$ such that adjacent or incident elements receive different colours.
Kang, Ross J. +2 more
core +6 more sources
On Uniquely 3-Colorable Plane Graphs without Adjacent Faces of Prescribed Degrees
Mathematics, 2019 A graph G is uniquely k-colorable if the chromatic number of G is k and G has only one k-coloring up to the permutation of the colors. For a plane graph G, two faces f 1 and f 2 of G are adjacent ( i , j )-faces if d ( f 1 ) = i,
Zepeng Li +4 more
doaj +1 more source
On Some Types of Matrices for Fan Plane Graph and Their Dual
Tikrit Journal of Pure Science, 2023 This work aims to discuss the adjacency matrices, Incidence matrix and Degree matrix of some types plane graphs we usually used them, as complete graphs, cycle graph,…,ect.
Haneen Mohammed Adil, Israa Munir Tawfik
doaj +1 more source
ROBUST AND ACCURATE PLANE SEGMENTATION FROM POINT CLOUDS OF STRUCTURED SCENES [PDF]
ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 2020 Plane segmentation from the point cloud is an important step in various types of geo-information related to human activities. In this paper, we present a new approach to accurate segment planar primitives simultaneously by transforming it into the best ...
P. Hu, Y. Liu, M. Tian, M. Hou
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Spanning Plane Subgraphs of 1‐Plane Graphs
Journal of Graph TheoryABSTRACTA graph drawn on the plane is called 1‐plane if each edge is crossed at most once by another edge. In this paper, we show that every 4‐edge‐connected 1‐plane graph has a connected spanning plane subgraph. We also show that there exist infinitely many 4‐connected 1‐plane graphs that have no 2‐connected spanning plane subgraphs.
Kenta Noguchi +2 more
openaire +2 more sources