If a geometric representation of a graph G can be drawn on a plane in such a way that no two edges of G intersect each other ,then G is said a planar graph. In this paper an approach to devise a planar graph using Kuratowski's two non-planar graph K5 (with minimum number of ...
The Kuratowski graphs K5 and K3,3 are fundamental non-planar graphs. We are interested in obtaining all their distinct 2-cell embeddings on orientable surfaces. The 2-cell embeddings of K5 and K3,3 on the torus are well-known. Using a constructive approach of expanding from minors, we ob...
We consider the class T of 2-connected non-planar K3,3-subdivision-free graphs that are embeddable in the torus. We show that any graph in T admits a unique decomposition as a basic toroidal graph (the toroidal core) where the edges are replaced by two-pole networks constructed from 2-...
The Planar Ramsey Numbers PR (K4-e, Kl) The planar Ramsey number PR (H1, H2) is the smallest integer n such that any planar graph on n vertices contains a copy of H1 or its complement contains a ... YQ Sun,YL Wu,Z Rui,... - 《American Journal of Computational Mathematics》 被...
A graph is called 3K3-free if it does not contain 3K3 as a subgraph. In this paper, we present a sharp upper bound on the Q-index of 3K3-free graphs of order n≥453, and characterize the unique extremal graph which attains the bound....
[16]FU H L,HUANG K C,YEN C H.The linear 3-arboricity of Knand Kn,n[J].Discrete Math,2008,308:3816-3823. [17]YEN C H,FU H L.Linear 3-arboricity of the balanced complete multipartite graph[J].Appl Math,2007,50:33-46.©...
The circumference of a graph with no K3,t-minor, II The class of graphs with no K3;t-minors, t>=3, contains all planar graphs and plays an important role in graph minor theory. In 1992, Seymour and Thomas co... G Chen,X Yu,W Zang - Academic Press, Inc. ...
A clique-coloring of a given graphGis a coloring of the vertices ofGsuch that no maximal clique of size at least two is monocolored. The clique-chromatic number ofGis the least number of colors for whichGadmits a clique-coloring. It has been proved that every planar graph is 3-clique ...
The oral presentations were organized in eight lecture sessions with the following topics: micro-aerial vehicles, tracking, graph sparsification, 3D segmentation and interpretation, object and place recognition, exploration, localization and mapping, and applications. The sessions topics are an indicator ...
The chemical construction of a macromolecular K 3,3 graph, a renowned triply-fused tetracyclic, non-planar construction with various inspiring topological properties, has been undertaken by the ESA-CF protocol. Remarkably, an equivalent topology has been identified in naturally occurring cyclic ...