2 research outputs found
Strongly light subgraphs in the 1-planar graphs with minimum degree 7
A graph is {\em -planar} if it can be drawn in the plane such that every
edge crosses at most one other edge. A connected graph is {\em strongly
light} in a family of graphs , if there exists a constant
, such that every graph in contains a subgraph
isomorphic to with for all . In this
paper, we present some strongly light subgraphs in the family of -planar
graphs with minimum degree~.Comment: 6 pages, 6 figures,
http://amc-journal.eu/index.php/amc/article/view/564. in Ars Mathematica
Contemporanea, 201
A note on 1-planar graphs with minimum degree 7
It is well-known that 1-planar graphs have minimum degree at most 7, and not
hard to see that some 1-planar graphs have minimum degree exactly 7. In this
note we show that any such 1-planar graph has at least 24 vertices, and this is
tight.Comment: 4 page