A nonplanar graph G is near-planar if it contains an edge e such that G − e is planar. The problem of determining the crossing number of a near-planar graph is exhibited from di...
For a non-negative integer T, we prove that the independence number of a graph G = (V, E) in which every vertex belongs to at most T triangles is at least uV f(d(u), T) where d(u)...
A strong oriented k-coloring of an oriented graph G is a homomorphism from G to H having k vertices labelled by the k elements of an abelian additive group M, such that for any p...
Determining the maximum number of D-dimensional spheres of radius r that can be adjacent to a central sphere of radius r is known as the Kissing Number Problem (KNP). The problem ...
Sergei Kucherenko, Pietro Belotti, Leo Liberti, Ne...
: For two given graphs G1 and G2, the Ramsey number R(G1, G2) is the smallest integer n such that for any graph G of order n, either G contains G1 or the complement of G contains G...
T. C. Edwin Cheng, Yaojun Chen, Yunqing Zhang, C. ...