Computing the genus of the 2-amalgamations of graphs

Abstract

The above authors [2] and S. Stahl [3] have shown that if a graphG is the 2-amalgamation of subgraphsG 1 andG 2 (namely ifG=G 1G 2 andG 1G 2={x, y}, two distinct points) then the orientable genus ofG,γ(G), is given byγ(G)=γ(G 1)+γ(G 2)+ε, whereε=0,1 or −1. In this paper we sharpen that result by giving a means by whichε may be computed exactly. This result is then used to give two irreducible graphs for each orientable surface.

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References

  1. [1]

    S. Alpert, The genera of amalgamations of graphs,Trans. Am. Math. Soc. 178 (1973), 1–39.

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  2. [2]

    R. Decker, H. Glover andJ. P. Huneke, The genus of the 2-amalgamations of graphs,Journal of Graph Theory 5 (1981), 95–102.

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  3. [3]

    S. Stahl, Permutation-partition pairs: a combinatorial generalization of graph embedding.Trans. Am. Math. Soc. 259 (1980), 129–145.

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Decker, R.W., Glover, H.H. & Huneke, J.P. Computing the genus of the 2-amalgamations of graphs. Combinatorica 5, 271–282 (1985). https://doi.org/10.1007/BF02579241

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AMS subject classification (1980)

  • 05 C 10
  • 57 M 15