Abstract
Let G be a finite r-graph where two (distinct) vertices are joined by at most r lines and let [G] denote the degree sequence of G. If s is an integer, s ≥ r + 1, then we prove that a degree sequence [K1] has a realizing s-graph containing graph G if and only if the sequence [ki] - [H] is s-realizable for all subgraphs H of G.
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References
Fulkerson, D. R., Hoffman, A. J., and McAndrew, M. H., "Some Properties of Graphs with Multiple Edges," Canad. J. Math., 17 (1965), 166–177.
Kundu, S., "A Factorization Theorem for Certain Class of Graphs," Discrete Math., to appear.
Tutte, W. T., "A Short Proof of the Factor Theorem for Finite Graphs," Canad. J. Math., 6 (1954), 347–352.
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© 1974 Springer-Verlag Berlin
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Kundu, S. (1974). A graphical realization problem. In: Bari, R.A., Harary, F. (eds) Graphs and Combinatorics. Lecture Notes in Mathematics, vol 406. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066452
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DOI: https://doi.org/10.1007/BFb0066452
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