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GRAPHICAL CONFLICT I: A NEW CLASS OF EXTREMAL PROBLEMS
Author(s) -
Harary Frank,
Kabell Jerald A.
Publication year - 1979
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1111/j.1749-6632.1979.tb32800.x
Subject(s) - exemplification , analogy , quotient , class (philosophy) , mathematics , graph , point (geometry) , combinatorics , computer science , discrete mathematics , mathematical economics , epistemology , artificial intelligence , philosophy , geometry
S ummary Inspired by the analogy with the three traditional types of conflict in psychology (approach/approach, approach/avoid, and avoid/avoid), we consider corresponding types of extremal problems in graph theory. These are translated into the determination of extremal values of the product or quotient of two graphical parameters, subject to given constraints. For purposes of exemplification, we study and determine both the exact solution and the extremal graphs for several products and quotients which include confrontations of (a) point‐ and line‐independence and covering, (b) connectivity and coloring, (c) covering and connectivity. We conclude with an indication of several unsolved problems for future research.