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  • 1985-1989  (3)
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Year
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  • 1
    Electronic Resource
    Electronic Resource
    Bounding the diameter of distance-regular graphs (1988)
    Springer
    Combinatorica 8 (1988), S. 333-343 
    Details
    ISSN: 1439-6912
    Keywords: 05 C 99
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract LetG be a connected distance-regular graph with valencyk〉2 and diameterd, but not a complete multipartite graph. Suppose thatθ is an eigenvalue ofG with multiplicitym and thatθ≠±k. We prove that bothd andk are bounded by functions ofm. This implies that, ifm〉1 is given, there are only finitely many connected, co-connected distance-regular graphs with an eigenvalue of multiplicitym.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02189090
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Tournaments with prescribed regular automorphism group (1986)
    Springer
    Aequationes mathematicae 30 (1986), S. 55-64 
    Details
    ISSN: 1420-8903
    Keywords: Primary 05C25
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A tournamentX is a TRR for a groupG if (a)G acts regularly on the vertices ofX and (b) Aut(X) is isomorphic toG. We correct some previous work of Babai and Imrich by showing thatZ 2 3 andZ 3 3 are the only groups of odd order without TRR's. Our methods are perhaps of independent interest, since we use a probabilistic approach.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02189910
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    The chromatic connectivity of graphs (1988)
    Springer
    Graphs and combinatorics 4 (1988), S. 229-233 
    Details
    ISSN: 1435-5914
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A graphG ischromatically k-connected if every vertex cutset induces a subgraph with chromatic number at leastk. This concept arose in some work, involving the third author, on Ramsey Theory. (For the reference, see the text.) Here we begin the study of chromatic connectivity for its own sake. We show thatG is chromaticallyk-connected iff every homomorphic image of it isk-connected. IfG has no triangles then it is at most chromatically 1-connected, but we prove that the Kneser graphs provide examples ofK 4-free graphs with arbitrarily large chromatic connectivity. We also verify thatK 4-free planar graphs are at most chromatically 2-connected.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01864163
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    Paper (German National Licenses)
    Fulltext
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