A graph is called 1-planar if it can be drawn in the plane so that each its edge is crossed by
at most one other edge. In the paper, we study the existence of subgraphs of bounded …

It is well known that every planar graph contains a vertex of degree at most 5. A theorem of
Kotzig states that every 3-connected planar graph contains an edge whose endvertices …

One of the central areas of graph theory is coloring, which is partitioning discrete objects into
simpler sub-objects. The development of the theory of planar graphs coloring, as well as that …

A graph H is light in a given class of graphs if there is a constant w such that every graph of
the class which has a subgraph isomorphic to H also has a subgraph isomorphic to H whose …

A graph H is defined to be light in a family H of graphs if there exists a finite number φ (H, H)
such that each G∈ H which contains H as a subgraph, contains also a subgraph K≅ H such …

Back in 1922, Franklin proved that every 3-polytope P 5 with minimum degree 5 has a 5-
vertex adjacent to two vertices of degree at most 6, which is tight. This result has been …

A connected graph H is said to be light in the family of graphs H if there exists a positive
integer k such that each graph G∈ H that contains an isomorphic copy of H contains a …

A graph is called 1-planar if there exists its drawing in the plane such that each edge
contains at most one crossing. We prove that each 1-planar graph of minimum degree 7 …

The discharging method in combinatorial geometry and the Page 328 http://dx. doi. org/10.1090/conm/453/08806
Contemporary Mathematics Volume 453, 2008 The discharging method in combinatorial …

A graph H is defined to be light in a family H of graphs if there exists a finite number w (H, H)
such that each G∈ H which contains H as a subgraph, contains also a subgraph K≅ H such …