The relative neighbourhood graph of a finite planar set

Graphs omitting a finite set of cycles

✍ Cherlin, Gregory; Shi, Niandong 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 300 KB 👁 2 views

We prove that for C a finite set of cycles, there is a universal C-free graph if and only if C consists precisely of all the odd cycles of order less than same specified bound.

Harmonic measure of the planar Cantor se

Harmonic measure of the planar Cantor set from the viewpoint of graph theory

✍ Massimo A. Picardello; Mitchell H. Taibleson; Wolfgang Woess 📂 Article 📅 1992 🏛 Elsevier Science 🌐 English ⚖ 890 KB

This paper outlines Q ,+tpi-+ theoretical approach to the study of the harmonic measure on the two-dimensional Canto: set. The Cantor set is regarded as the space of ends of a (nonplanar) graph with d t:ee-like structure. The method is based upon the combinatorics of the random walk with internal st

The Relative Maximum Genus of a Graph

✍ C.P. Bonnington 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 422 KB

Coloring the square of a planar graph

✍ Jan van den Heuvel; Sean McGuinness 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 125 KB 👁 2 views

## Abstract We prove that for any planar graph __G__ with maximum degree Δ, it holds that the chromatic number of the square of __G__ satisfies χ(__G__^2^) ≤ 2Δ + 25. We generalize this result to integer labelings of planar graphs involving constraints on distances one and two in the graph. © 2002

On the depth of a planar graph

✍ Vinay G. Kane; Sanat K. Basu 📂 Article 📅 1976 🏛 Elsevier Science 🌐 English ⚖ 525 KB

A criterion for the planarity of a graph

✍ Jerome R. Breitenbach 📂 Article 📅 1986 🏛 John Wiley and Sons 🌐 English ⚖ 146 KB 👁 1 views

In a recent paper, Carsten Thomassen [Carsten Thomassen, Planarity and duality of finite and infinite graphs. J. Combinatorial Theory Ser. B 29 (1980) 244-2711 has shown that a number of criteria for the planarity of a graph can be reduced to that of Kuratowski. Here we present another criterion whi