Transformations for maximal planar graphs with minimum degree five

1995 ◽  
pp. 366-371
Author(s):  
Jean Hardouin Duparc ◽  
Philippe Rolland
Keyword(s):  
Planar Graphs ◽  
Minimum Degree

Light Edges in 3-Connected 2-Planar Graphs With Prescribed Minimum Degree

2016 ◽  
Vol 41 (3) ◽  
pp. 1265-1274
Author(s):  
Zai Ping Lu ◽  
Ning Song
Keyword(s):  
Planar Graphs ◽  
Minimum Degree

scholarly journals The 7-cycle C7 is light in the family of planar graphs with minimum degree 5

2007 ◽  
Vol 307 (11-12) ◽  
pp. 1430-1435 ◽  
Author(s):  
T. Madaras ◽  
R. Škrekovski ◽  
H.-J. Voss
Keyword(s):  
Planar Graphs ◽  
Minimum Degree ◽  
The Family

scholarly journals The structure and the list 3-dynamic coloring of outer-1-planar graphs

2021 ◽  
Vol vol. 23, no. 3 (Graph Theory) ◽  
Author(s):  
Yan Li ◽  
Xin Zhang
Keyword(s):  
Planar Graph ◽  
Chromatic Number ◽  
Upper Bound ◽  
Local Structure ◽  
Planar Graphs ◽  
Minimum Degree ◽  
Outer Region ◽  
The Other ◽  
Structural Theorem ◽  
Other Hand

An outer-1-planar graph is a graph admitting a drawing in the plane so that all vertices appear in the outer region of the drawing and every edge crosses at most one other edge. This paper establishes the local structure of outer-1-planar graphs by proving that each outer-1-planar graph contains one of the seventeen fixed configurations, and the list of those configurations is minimal in the sense that for each fixed configuration there exist outer-1-planar graphs containing this configuration that do not contain any of another sixteen configurations. There are two interesting applications of this structural theorem. First of all, we conclude that every (resp. maximal) outer-1-planar graph of minimum degree at least 2 has an edge with the sum of the degrees of its two end-vertices being at most 9 (resp. 7), and this upper bound is sharp. On the other hand, we show that the list 3-dynamic chromatic number of every outer-1-planar graph is at most 6, and this upper bound is best possible.

scholarly journals A note on 1-planar graphs with minimum degree 7

2021 ◽  
Vol 289 ◽  
pp. 230-232
Author(s):  
Therese Biedl
Keyword(s):  
Planar Graphs ◽  
Minimum Degree

On Light Edges and Triangles in Planar Graphs of Minimum Degree Five

2006 ◽  
Vol 170 (1) ◽  
pp. 19-24 ◽  
Author(s):  
Oleg V. Borodin ◽  
Daniel P. Sanders
Keyword(s):  
Planar Graphs ◽  
Minimum Degree

Light edges in 1-planar graphs with prescribed minimum degree

2012 ◽  
Vol 32 (3) ◽  
pp. 545 ◽  
Author(s):  
Dávid Hudák ◽  
Peter Šugerek
Keyword(s):  
Planar Graphs ◽  
Minimum Degree

Light subgraphs in the family of 1-planar graphs with high minimum degree

2011 ◽  
Vol 28 (6) ◽  
pp. 1155-1168 ◽  
Author(s):  
Xin Zhang ◽  
Gui Zhen Liu ◽  
Jian Liang Wu
Keyword(s):  
Planar Graphs ◽  
Minimum Degree ◽  
The Family

Light subgraphs in planar graphs of minimum degree 4 and edge-degree 9

2003 ◽  
Vol 44 (4) ◽  
pp. 261-295 ◽  
Author(s):  
B. Mohar ◽  
R. ?krekovski ◽  
H.-J. Voss
Keyword(s):  
Planar Graphs ◽  
Minimum Degree

scholarly journals Computing Large Matchings in Planar Graphs with Fixed Minimum Degree

2009 ◽  
pp. 872-881
Author(s):  
Robert Franke ◽  
Ignaz Rutter ◽  
Dorothea Wagner
Keyword(s):  
Planar Graphs ◽  
Minimum Degree

scholarly journals On local properties of 1-planar graphs with high minimum degree

2011 ◽  
Vol 4 (2) ◽  
pp. 245-254 ◽  
Author(s):  
Dávid Hudák ◽  
Tomáš Madaras
Keyword(s):  
Planar Graphs ◽  
Minimum Degree ◽  
Local Properties
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