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  • 1
    Electronic Resource
    Electronic Resource
    On the Fractional Intersection Number of a Graph (1999)
    Springer
    Graphs and combinatorics 15 (1999), S. 341-351 
    Details
    ISSN: 1435-5914
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract.  An intersection representation of a graph G is a function f:V(G)→2S (where S is any set) with the property that uv∈E(G) if and only if f(u)∩f(v)≠∅. The size of the representation is |S|. The intersection number of G is the smallest size of an intersection representation of G. The intersection number can be expressed as an integer program, and the value of the linear relaxation of that program gives the fractional intersection number. This is in consonance with fractional versions of other graph invariants such as matching number, chromatic number, edge chromatic number, etc.  We examine cases where the fractional and ordinary intersection numbers are the same (interval and chordal graphs), as well as cases where they are wildly different (complete multipartite graphs). We find the fractional intersection number of almost all graphs by considering random graphs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s003730050068
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  • 2
    Book
    Book
    Tolerance graphs /; 89 (2004)
    Cambridge [u.a.] :Cambridge Univ. Press,
    Details
    Title: Tolerance graphs /; 89
    Author: Golumbic, Martin Charles
    Contributer: Trenk, Ann N.
    Edition: 1
    Publisher: Cambridge [u.a.] :Cambridge Univ. Press,
    Year of publication: 2004
    Pages: XII, 265 S. : , graph. Darst.
    Series Statement: Cambridge studies in advanced mathematics 89
    ISBN: 0-521-82758-2
    Type of Medium: Book
    Language: English
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