Results 51 to 60 of about 1,442,532 (348)

Total Coloring of Claw-Free Planar Graphs

open access: yesDiscussiones Mathematicae Graph Theory, 2022
A total coloring of a graph is an assignment of colors to both its vertices and edges so that adjacent or incident elements acquire distinct colors. Let Δ(G) be the maximum degree of G.
Liang Zuosong
doaj   +1 more source

Planar Octilinear Drawings with One Bend Per Edge [PDF]

open access: yes, 2014
In octilinear drawings of planar graphs, every edge is drawn as an alternating sequence of horizontal, vertical and diagonal ($45^\circ$) line-segments. In this paper, we study octilinear drawings of low edge complexity, i.e., with few bends per edge. A $
A. Garg   +16 more
core   +2 more sources

A Sufficient Condition for Planar Graphs of Maximum Degree 6 to be Totally 7-Colorable

open access: yesDiscrete Dynamics in Nature and Society, 2020
A total k-coloring of a graph is an assignment of k colors to its vertices and edges such that no two adjacent or incident elements receive the same color.
Enqiang Zhu, Yongsheng Rao
doaj   +1 more source

Star edge coloring of $ K_{2, t} $-free planar graphs

open access: yesAIMS Mathematics, 2023
The star chromatic index of a graph $ G $, denoted by $ \chi{'}_{st}(G) $, is the smallest number of colors required to properly color $ E(G) $ such that every connected bicolored subgraph is a path with no more than three edges.
Yunfeng Tang , Huixin Yin , Miaomiao Han
doaj   +1 more source

A Planarity Criterion for Graphs [PDF]

open access: yesSIAM Journal on Discrete Mathematics, 2015
It is proven that a connected graph is planar if and only if all its cocycles with at least four edges are "grounded" in the graph. The notion of grounding of this planarity criterion, which is purely combinatorial, stems from the intuitive idea that with planarity there should be a linear ordering of the edges of a cocycle such that in the two ...
Kosta Došen, Zoran Petric
openaire   +3 more sources

From light edges to strong edge-colouring of 1-planar graphs [PDF]

open access: yesDiscrete Mathematics & Theoretical Computer Science, 2020
A strong edge-colouring of an undirected graph $G$ is an edge-colouring where every two edges at distance at most~$2$ receive distinct colours. The strong chromatic index of $G$ is the least number of colours in a strong edge-colouring of $G$.
Julien Bensmail   +3 more
doaj   +1 more source

Planar Transitive Graphs [PDF]

open access: yesThe Electronic Journal of Combinatorics, 2018
We prove that the first homology group of every planar locally finite transitive graph $G$ is finitely generated as an $\Aut(G)$-module and we prove a similar result for the fundamental group of locally finite planar Cayley graphs. Corollaries of these results include Droms's theorem that planar groups are finitely presented and Dunwoody's theorem that
openaire   +3 more sources

An algorithm of graph planarity testing and cross minimization [PDF]

open access: yesComputer Science Journal of Moldova, 2007
This paper presents an overview on one compartment from the graph theory, called graph planarity testing. It covers the fundamental concepts and important work in this area.
Vitalie Cotelea, Stela Pripa
doaj  

NIC-planar graphs

open access: yesDiscrete Applied Mathematics, 2017
A graph is NIC-planar if it admits a drawing in the plane with at most one crossing per edge and such that two pairs of crossing edges share at most one common end vertex. NIC-planarity generalizes IC-planarity, which allows a vertex to be incident to at most one crossing edge, and specializes 1-planarity, which only requires at most one crossing per ...
Franz J. Brandenburg   +4 more
openaire   +2 more sources

Contact Representations of Graphs in 3D

open access: yes, 2015
We study contact representations of graphs in which vertices are represented by axis-aligned polyhedra in 3D and edges are realized by non-zero area common boundaries between corresponding polyhedra. We show that for every 3-connected planar graph, there
A Bezdek   +17 more
core   +1 more source

Home - About - Disclaimer - Privacy