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https://doi.org/10.1007/978-3-663-10855-9crossing number are introduced and related to one another. We then deal with topological techniques in the theory of chromatic numbers, and state a very ambitious meta-conjecture which is quite useful in generating true theorems. In closing, we attempt to suggest appropriate directions for further r
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https://doi.org/10.1007/978-3-322-87301-9s, (2) we can determine the first p moments by counting closed walks and then find the spectrum from the moments, or (3) we can use certain subgraphs to determine the coefficients of the characteristic polynomial and then find its roots..In practice, however, all of these approaches may prove to be
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https://doi.org/10.1007/978-3-663-01491-1n independent set of vertices that contains at least 1/4 of the vertices of the graph. The purpose of this paper is to give an algorithm that produces an independent set in a planar graph that contains more than 2/9 of the vertices of the graph.
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https://doi.org/10.1007/978-3-476-03772-5induce 1-factorizations of complete graphs. It is easy to show that these 1-factorizations possess enough symmetry to insure that if {F., F.} and {F., F.} are pairs of distinct 1-factors from such a 1-factorization, then the cycle structures of F. ∪ F. and F. ∪ F. are identical. The method is applie
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https://doi.org/10.1007/978-3-663-02714-0er well-known graphical invariants is discussed, and ζ is evaluated for a variety of special classes of graphs. A simple algorithm is developed for determining ζ in the case of a tree, and it is shown that this tree algorithm can be generalized to yield ζ for any connected graph. Degree conditions a
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