scholarly journals Light graphs in planar graphs of large girth

2016 ◽  
Vol 36 (1) ◽  
pp. 227
Author(s):  
Peter Hudák ◽  
Mária Maceková ◽  
Tomas Madaras ◽  
Pavol Široczki
Keyword(s):  
Planar Graphs ◽  
Large Girth

scholarly journals Acyclic edge coloring of planar graphs with large girth

2009 ◽  
Vol 410 (47-49) ◽  
pp. 5196-5200 ◽  
Author(s):  
Dongxiao Yu ◽  
Jianfeng Hou ◽  
Guizhen Liu ◽  
Bin Liu ◽  
Lan Xu
Keyword(s):  
Planar Graphs ◽  
Edge Coloring ◽  
Acyclic Edge Coloring ◽  
Large Girth

scholarly journals Linear coloring of planar graphs with large girth

2009 ◽  
Vol 309 (18) ◽  
pp. 5678-5686 ◽  
Author(s):  
André Raspaud ◽  
Weifan Wang
Keyword(s):  
Planar Graphs ◽  
Large Girth

scholarly journals Circular Chromatic Number of Signed Graphs

10.37236/9938 ◽  
2021 ◽  
Vol 28 (2) ◽  
Author(s):  
Reza Naserasr ◽  
Zhouningxin Wang ◽  
Xuding Zhu
Keyword(s):  
Chromatic Number ◽  
Planar Graphs ◽  
Simple Graph ◽  
Signed Graph ◽  
Signed Graphs ◽  
Outerplanar Graphs ◽  
Circular Chromatic Number ◽  
Basic Properties ◽  
Large Girth ◽  
Sigma E

A signed graph is a pair $(G, \sigma)$, where $G$ is a graph (loops and multi edges allowed) and $\sigma: E(G) \to \{+, -\}$ is a signature which assigns to each edge of $G$ a sign. Various notions of coloring of signed graphs have been studied. In this paper, we extend circular coloring of graphs to signed graphs. Given a signed graph $(G, \sigma)$ with no positive loop, a circular $r$-coloring of $(G, \sigma)$ is an assignment $\psi$ of points of a circle of circumference $r$ to the vertices of $G$ such that for every edge $e=uv$ of $G$, if $\sigma(e)=+$, then $\psi(u)$ and $\psi(v)$ have distance at least $1$, and if $\sigma(e)=-$, then $\psi(v)$ and the antipodal of $\psi(u)$ have distance at least $1$. The circular chromatic number $\chi_c(G, \sigma)$ of a signed graph $(G, \sigma)$ is the infimum of those $r$ for which $(G, \sigma)$ admits a circular $r$-coloring. For a graph $G$, we define the signed circular chromatic number of $G$ to be $\max\{\chi_c(G, \sigma): \sigma \text{ is a signature of $G$}\}$.  We study basic properties of circular coloring of signed graphs and develop tools for calculating $\chi_c(G, \sigma)$. We explore the relation between the circular chromatic number and the signed circular chromatic number of graphs, and present bounds for the signed circular chromatic number of some families of graphs. In particular,  we determine the supremum of the signed circular chromatic number of $k$-chromatic graphs of large girth, of simple bipartite planar graphs, $d$-degenerate graphs, simple outerplanar graphs and series-parallel graphs. We construct a signed planar simple graph whose circular chromatic number is $4+\frac{2}{3}$. This is based and improves on a signed graph built by Kardos and Narboni as a counterexample to a conjecture of Máčajová, Raspaud, and Škoviera. 

scholarly journals Acyclic Colourings of Planar Graphs with Large Girth

1999 ◽  
Vol 60 (2) ◽  
pp. 344-352 ◽  
Author(s):  
O. V. Borodin ◽  
A. V. Kostochka ◽  
D. R. Woodall
Keyword(s):  
Planar Graphs ◽  
Large Girth

scholarly journals Strong chromatic index of planar graphs with large girth

2014 ◽  
Vol 34 (4) ◽  
pp. 723 ◽  
Author(s):  
Gerard Jennhwa Chang ◽  
Mickael Montassier ◽  
Arnaud Pecher ◽  
André Raspaud
Keyword(s):  
Planar Graphs ◽  
Chromatic Index ◽  
Strong Chromatic Index ◽  
Large Girth

The List L(2, 1)-Labeling of Planar Graphs with Large Girth

2020 ◽  
pp. 501-512
Author(s):  
Zhu Haiyang ◽  
Zhu Junlei ◽  
Liu Ying ◽  
Wang Shuling ◽  
Huang Danjun ◽  
...  
Keyword(s):  
Planar Graphs ◽  
Large Girth

scholarly journals On (p,1)-total labelling of plane graphs with independent crossings

Filomat ◽  
2012 ◽  
Vol 26 (6) ◽  
pp. 1091-1100 ◽  
Author(s):  
Xin Zhang ◽  
Guizhen Liu ◽  
Yong Yu
Keyword(s):  
Planar Graph ◽  
Planar Graphs ◽  
Maximum Degree ◽  
Discrete Math ◽  
Plane Graph ◽  
Plane Graphs ◽  
High Maximum ◽  
Crossed Pair ◽  
Large Girth

Two distinct crossings are independent if the end-vertices of the crossed pair of edges are mutually different. If a graph G has a drawing in the plane so that every two crossings are independent, then we call G a plane graph with independent crossings or IC-planar graph for short. In this paper, it is proved that the (p, 1)-total labelling number of every IC-planar graph G is at most ?(G) + 2p ? 2 provided that ?(G) ? ? and 1(G) ? 1, where (?, 1) ? {(6p + 2, 3), (4p + 2, 4), (2p + 5, 5)}. As a consequence, we generalize and improve some results obtained in [F. Bazzaro, M. Montassier, A. Raspaud, (d, 1)-Total labelling of planar graphs with large girth and high maximum degree, Discrete Math. 307 (2007) 2141-2151].

scholarly journals $k$-forested coloring of planar graphs with large girth

2010 ◽  
Vol 86 (10) ◽  
pp. 169-173 ◽  
Author(s):  
Xin Zhang ◽  
Guizhen Liu ◽  
Jian-Liang Wu
Keyword(s):  
Planar Graphs ◽  
Large Girth
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