scholarly journals On Different "Middle Parts" of a Tree

10.37236/6408 ◽  
2018 ◽  
Vol 25 (3) ◽  
Author(s):  
Heather Smith ◽  
László Székely ◽  
Hua Wang ◽  
Shuai Yuan

We determine the maximum distance between any two of the center, centroid, and subtree core among trees with a given order. Corresponding results are obtained for trees with given maximum degree and also for trees with given diameter. The problem of the maximum distance between the centroid and the subtree core among trees with given order and diameter becomes difficult. It can be solved in terms of the problem of minimizing the number of root-containing subtrees in a rooted tree of given order and height. While the latter problem remains unsolved, we provide a partial characterization of the extremal structure.

10.37236/5895 ◽  
2016 ◽  
Vol 23 (3) ◽  
Author(s):  
Ligang Jin ◽  
Yingli Kang ◽  
Eckhard Steffen

The only remaining case of a well known conjecture of Vizing states that there is no planar graph with maximum degree 6 and edge chromatic number 7. We introduce parameters for planar graphs,  based on the degrees of the faces, and study the question whether there are upper bounds for these parameters for planar edge-chromatic critical graphs. Our results provide upper bounds on these parameters for smallest counterexamples to Vizing's conjecture, thus providing a partial characterization of such graphs, if they exist.For $k \leq 5$ the results give insights into the structure of planar edge-chromatic critical graphs.


2004 ◽  
Vol 4 (1) ◽  
pp. 62-89 ◽  
Author(s):  
Andreas Hoffjan

This study introduces content analysis as a method of examining the accountant's role. The empirical study is based on 73 advertisements, which are directed primarily at employees who are affected by the management accountant's work. The findings of the study indicate that the subject of accountancy is used particularly in connection with promises of “cost reduction.” Consequently, the majority of advertisements use the accountant stereotype of “savings personified.” In a professional context, the work ethic of the management accountant is given particular emphasis in the advertisements. He/she identifies him/herself with his/her task to the maximum degree, is regarded as loyal to his/her company and, for the most part, is well organized in his/her work. However, the characterization of the management accountant as a well disciplined company-person conflicts with the negative portrayal of his/her professional qualities. In advertisements, the management accountant is portrayed as a rather inflexible, passive, and uncreative specialist who, as a result of these qualities, often demotivates others. The personal characteristics of the management accountant are shown in a negative light. This gives him/her the unappealing image of a humorless, envious, dissociated, and ascetic corporate-person.


2010 ◽  
Vol 108 (10) ◽  
pp. 323-329 ◽  
Author(s):  
Marti F. A. Bierhuizen ◽  
Moniek de Wit ◽  
Carin A. R. L. Govers ◽  
Willem van Dijk

1966 ◽  
Vol 241 (7) ◽  
pp. 1530-1536
Author(s):  
Marcos Rojkind ◽  
Olga O. Blumenfeld ◽  
Paul M. Gallop

1980 ◽  
Vol 255 (11) ◽  
pp. 5468-5474 ◽  
Author(s):  
R.J. Kirschner ◽  
C.S. Federiuk ◽  
J.P. Ford ◽  
J.A. Shafer

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