Parity of numbers of crossings for complete -partite graphs
Partial confluence of maps onto graphs and inverse limits of single graphs
Partitions of some planar graphs into two linear forests
A linear forest is a forest in which every component is a path. It is known that the set of vertices V(G) of any outerplanar graph G can be partitioned into two disjoint subsets V₁,V₂ such that induced subgraphs ⟨V₁⟩ and ⟨V₂⟩ are linear forests (we say G has an (LF, LF)-partition). In this paper, we present an extension of the above result to the class of planar graphs with a given number of internal vertices (i.e., vertices that do not belong to the external face at a certain fixed embedding of...
Path-Neighborhood Graphs
A path-neighborhood graph is a connected graph in which every neighborhood induces a path. In the main results the 3-sun-free path-neighborhood graphs are characterized. The 3-sun is obtained from a 6-cycle by adding three chords between the three pairs of vertices at distance 2. A Pk-graph is a path-neighborhood graph in which every neighborhood is a Pk, where Pk is the path on k vertices. The Pk-graphs are characterized for k ≤ 4.
Paths of low weight in planar graphs
The existence of paths of low degree sum of their vertices in planar graphs is investigated. The main results of the paper are: 1. Every 3-connected simple planar graph G that contains a k-path, a path on k vertices, also contains a k-path P such that for its weight (the sum of degrees of its vertices) in G it holds 2. Every plane triangulation T that contains a k-path also contains a k-path P such that for its weight in T it holds 3. Let G be a 3-connected simple planar graph of circumference...
Percolation, Perimetry, Planarity.
Perfect codes in regular graphs
Permutations planaires généralisées
Planar decompositions and the crossing number of graphs with an excluded minor.
Planar drawings of higher-genus graphs.
Planar graphs as minimal resolutions of trivariate monomial ideals.
Planar graphs with topological constraints.
Planar graphs without 4-, 5- and 8-cycles are 3-colorable
In this paper we prove that every planar graph without 4, 5 and 8-cycles is 3-colorable.
Planar ordered sets of width two
Planar permutation graphs of paths
Planarity thresholds for two types of random subgraphs of the -cube
Planarizing graphs---a survey and annotated bibliography.
Plane trivalent trees and their patterns
The aim of this paper is to characterize the patterns of successive distances of leaves in plane trivalent trees, and give a very short characterization of their parity pattern. Besides, we count how many trees satisfy some given sequences of patterns.
Platonic hypermaps.
Plongements lipschitziens dans un espace pentagonal