On Structure of Some Plane Graphs with Application to Choosability

On structure of graphs embedded on surfaces of nonnegative characteristic with application to choosability

In this paper, we prove a structural theorem of Lebesgue’s type concerning some unavoidable con1gurations for graphs which can be embedded on surfaces of nonnegative characteristic and in which no two 3-cycles share a common vertex. As a corollary, we get a result about choosability of graphs embedded in surface of positive characteristic. c © 2002 Elsevier Science B.V. All rights reserved.

k-forested choosability of graphs with bounded maximum average degree

A proper vertex coloring of a simple graph is $k$-forested if the graph induced by the vertices of any two color classes is a forest with maximum degree less than $k$. A graph is $k$-forested $q$-choosable if for a given list of $q$ colors associated with each vertex $v$, there exists a $k$-forested coloring of $G$ such that each vertex receives a color from its own list. In this paper, we prov...

On 3-choosability of plane graphs without 3-, 8- and 9-cycles

Application of n-distance balanced graphs in distributing management and finding optimal logistical hubs

Optimization and reduction of costs in management of distribution and transportation of commodity are one of the main goals of many organizations. Using suitable models in supply chain in order to increase efficiency and appropriate location for support centers in logistical networks is highly important for planners and managers. Graph modeling can be used to analyze these problems and many oth...

Bounds on circular consecutive choosability

The circular consecutive choosability chcc(G) of a graph G has been recently introduced in [2]. In this paper we prove upper bounds on chcc for series-parallel graphs, planar graphs and k-choosable graphs. Our bounds are tight for classes of series-parallel graphs and k-choosable graphs for k ≥ 3. Then we study the circular consecutive choosability of generalized theta graphs. Lower bounds for ...