16.1: Motivation

Elementary Foundations: An Introduction to Topics in Discrete Mathematics · LibreTexts

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    From LibreTexts, under GNU Free Documentation, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    Example \(\PageIndex{1}\): Reducing redundancy.

    You have set up your own tree-fort communication system out of tin cans and strings. (See Worked Example 15.4.5.) However, peace has broken out and your communication system is underused. To address the crippling tin-can-and-string stilts shortage, you want to dismantle as much of your network as possible without disrupting communications.

    clipboard_eb97c6f8aea79a614522e3e963c95fd21.png
    Figure \(\PageIndex{1}\): TreeFort CommNet.

    Closed paths are redundant, as communication could be routed around such a path in two directions. So try to eliminate closed all paths; two possible solutions appear in Figure \(\PageIndex{2}\).

    clipboard_e470337e27eb1d93780485a3bd7f9c5d6.png
    (a) One possible result of removing redundancy.
    clipboard_e83586ee64cc05ff4d2aeaec9f1b1c05b.png
    (b) Another possible result of removing redundancy.
    Figure \(\PageIndex{2}\): TreeFort CommNet (after removing redundant communication paths).

    Remark \(\PageIndex{1}\)

    A more difficult modification of the above example would be to include the length of string in each communication link as a weight for that edge in the graph, and then try to determine a configuration that removes the most string from the network without disrupting communications.

    This page titled 16.1: Motivation was last modified on Tue, 01 Sep 2026 03:35:28 GMT and is shared under a GNU Free Documentation License 1.3 license and was authored, remixed, and/or curated by Jeremy Sylvestre via source content that was edited to the style and standards of the LibreTexts platform.