Z. Gao, The asymptotic number of rooted 2-connected triangular maps on a surface. J. Combin. Theory, Ser. B, 54 (1992) 102--112. Home/Search Document Not in Database Summary Related Articles Check |
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0-1 Laws for Maps - Bender, Compton, Richmond (Correct)
.... For (iv) and (vii) richness follows from Theorem 1 of [8] Large representativity for (i) ii) and (iii) follows from [5] Large representativity for (iv) follows from [5] and [7] Large representativity for (v) follows from [5] and [20] Large representativity for (vi) follows from [5] and [21]. Large representativity for (vii) follows from [5] and [22] The results in these references are all stated for rooted maps. However, by [29] they are valid as stated here. Remark. For maps on the plane, large representativity is trivial and so only richness needs to be verified for a 0 1 law ....
Zhi-Cheng Gao. The asymptotic number of rooted 2-connected triangular maps on a surface. J. Combin. Theory Ser. B, 54:102--112, 1992.
Almost All Rooted Maps Have Large Representativity - Bender, Gao, Richmond (1999) (1 citation) Self-citation (Gao) (Correct)
....rooted smooth maps [1] 3. rooted loopless maps, rooted simple maps and rooted 3 c triangulations [10] 4. rooted nonsingular maps and rooted 2 c maps (and the numbers are asymptotically equal) 5] 4 5. rooted triangular maps [7] 6. rooted triangulations, that is, rooted 2 c triangular maps [8]; 7. for certain D as discussed in [9] rooted maps with all face valencies in D (D = f3g is case 4) We expect that 3 c maps will be added to this list in the near future. The following proposition adds various families of quadrangulations to the list. Proposition 2. On any given surface S, ....
Z. Gao, The asymptotic number of rooted 2-connected triangular maps on a surface. J. Combin. Theory, Ser. B, 54 (1992) 102--112.
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