Graphs Theory

Assessing the Efficiency of Health Care Providers: A SOM Perspective

by Marina Resta

The Four-Color Map Theorem: "Kempe’s Fallacious Proof Repaired"

by Ibrahim Cahit

Further results can be found in the first 6 pages of my paper at arXiv :
http://arxiv.org/abs/0903.4108

A new non-computer direct algorithmic proof for the famous four color theorem based on new concept spiral-chain... more A new non-computer direct algorithmic proof for the famous four color theorem based on new concept spiral-chain coloring of maximal planar graphs has been proposed by the author in 2004 [6],[13]. Historical fallacious inductive proof of Kempe have been re-considered by many mathematicians whether it could be repaired. All attemps so far have been either modification of Kempe color switching argument or trying to show that random second-time coloring would not produce an impasse. In this
note we have shown that when Kempe’s argument fails by the trap of the incomplete four-coloring there is always a simple re-coloring of the nodes of a planar graph so that the undecided node colored properly. Hence our method may be considerd as an completion of fallacious Kempe’s inductive proof. Interesting enough, when we have resolved the impasse in the four coloring of the graphs, the solution end up again with two spirals (double-spirals) Kempe chains that cover all of the nodes.

Graphing the order of the sexes: Constructing, recalling, interpreting, and putting the self in gender difference graphs.

by Peter Hegarty

Graphs seem to connote facts more than words or tables do. Consequently, they seem unlikely places to spot implicit... more Graphs seem to connote facts more than words or tables do. Consequently, they seem unlikely places to spot implicit sexism at work. Yet, in 6 studies (N
741), women and men constructed (Study 1) and recalled (Study 2) gender difference graphs with men’s data first, and graphed powerful groups (Study
3) and individuals (Study 4) ahead of weaker ones. Participants who interpreted graph order as evidence of author “bias” inferred that the author graphed his or her own gender group first (Study 5). Women’s, but not men’s, preferences to graph men first were mitigated when participants graphed a difference between themselves and an opposite-sex friend prior to graphing gender differences (Study 6). Graph production and comprehension are affected by beliefs and suppositions about the groups represented in graphs to a greater degree than cognitive models of graph comprehension or realist models of scientific
thinking have yet acknowledged