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1.
In this paper, we study the chromatic sum functions of rooted nonseparable near-triangulations on the sphere and the projective plane. The chromatic sum function equations of such maps are obtained. From the chromatic sum equations of such maps, the enumerating function equations of such maps are derived. Applying chromatic sum theory, the enumerating problem of different sorts maps can be studied, and a new method of enumeration can be obtained. Moreover, an asymptotic evaluation and some explicit expression of enumerating functions are also derived. 相似文献
2.
In this paper, the chromatic sum functions of rooted biloopless nonseparable near-triangulations on the sphere and the projective plane are studied. The chromatic sum function equations of such maps are obtained. From the chromatic sum equations of such maps, the enumerating function equations of such maps are derived. An asymptotic evaluation and some explicit expression of enumerating functions are also derived. 相似文献
3.
Zhaoxiang Li 《Discrete Mathematics》2007,307(1):78-87
In this paper, we study the chromatic sum functions of rooted general maps on the sphere and the projective plane. The chromatic sum function equations of such maps are obtained. From the chromatic sum equations of such maps, the enumerating function equations of rooted loopless maps, bipartite maps and Eulerian maps are also derived. Moreover, some explicit expressions of enumerating functions are also derived. 相似文献
4.
In this paper, we study the rooted nonseparable maps on the sphere and the projective plane with the valency of root-face and the number of edges as parameters. Explicit expression of enumerating functions are obtained for such maps on the sphere and the projective plane. A parametric expression of the generating function is obtained for such maps on the projective plane, from which asymptotic evaluations are derived. Moreover, if the number of edges is sufficiently large, then almost all nonseparable maps on the projective plane are not triangulation. 相似文献
5.
A map is singular if each edge is on the same face on a sruface (i.e., those have only one face on a surface). Because any map with loop is not colorable, all maps here are assumed to be loopless. In this paper povides the explicit expression of chromatic sum functions for rooted singular maps on the projective plane, the torus and the Klein bottle. From the explicit expression of chromatic sum functions of such maps, the explicit expression of enum erating functions of such maps are also derived. 相似文献
6.
In this paper we study the chromatic sum functions for rooted nonseparable near-triangular maps on the projective plane. A chromatic sum equation for such maps is obtained. 相似文献
7.
W. T. Tutte 《Aequationes Mathematicae》1995,50(1-2):95-134
Summary This paper discusses some equations arising in the author's work on chromatic sums. The main results were presented in a series of papers extending from 1973 to 1982. The object here is to give a unified and simplified account of the elimination of unwanted variables from the initial equation, leading to the final identification of the desired chromatic sums as the coefficients in a power series satisfying a certain differential equation. 相似文献
8.
刘彦佩 《应用数学学报(英文版)》1989,5(2):169-175
In this paper, the number of combinatorially distinct rooted nonseparable outerplanar maps withm edges and the valency of the root-face being n is found to be(m-1)! (m-2) !:(n-1)!(n-2)! (m-n)!(m-n 1)!and, the number of rooted nonseparable outerplanar maps with m edges is also determined to be(2m-2)!:(m-1)!m!,which is just the number of distinct rooted plane trees with m-1 edges. 相似文献
9.
D. W. Barnette 《Israel Journal of Mathematics》1989,67(2):251-256
We characterize the 3-valent polyhedral maps in the projective plane whose graphs have a unique embedding in the projective
plane. This is done by demonstrating two forbidden subgraphs of the dual of these uniquely embeddable graphs. 相似文献
10.
11.
A planar map is a 2-cell embedding of a connected planar graph, loops and parallel edges allowed, on the sphere. A plane map is a planar map with a distinguished outside (“infinite”) face. An unrooted map is an equivalence class of maps under orientation-preserving homeomorphism, and a rooted map is a map with a distinguished oriented edge. Previously we obtained formulae for the number of unrooted planar n-edge maps of various classes, including all maps, non-separable maps, eulerian maps and loopless maps. In this article, using the same technique we obtain closed formulae for counting unrooted plane maps of all these classes and their duals. The corresponding formulae for rooted maps are known to be all sum-free; the formulae that we obtain for unrooted maps contain only a sum over the divisors of n. We count also unrooted two-vertex plane maps. 相似文献
12.
M.J. de la Puente 《Linear algebra and its applications》2011,435(7):1681-1795
13.
Enumeration of maps on the projective plane 总被引:1,自引:0,他引:1
1. IntroductionA lnap is rooted if an edge is distinguished togetl1er with an end and a side of the edge.An edge belo11ging to only one face is called double (or 8ingular by some author), al1 othersbelonging to exactly two faces are called s1ngle. The enumeration of rooted p1anar maps wasfirst introduced by Tutte['], Techniques originated by Tutte [2,3l for enumerating variousclasses of rooted Inaps on tIle sphere are here applied to the c1asses of alI rooted maps onthe projective plane. Th… 相似文献
14.
The notion of lexicographic sum is introduced in general categories. Existence criteria are derived, particularly for locally cartesian closed categories and for categories with suitable coproducts. Lexicographic sums satisfy a generalized associative law. More importantly, every morphism can be factored through the lexicographic sum of its fibres. This factorization and the two types of maps arising from it, fibre-trivial and fibre-faithful, are studied particularly for partially ordered sets and forT
1-spaces. 相似文献
15.
16.
In this paper we study the rooted loopless maps on the sphere and the projective plane with the valency of root-face and the number of edges as parameters. Explicit expression of enumerating function is obtained for such maps on the sphere and the projective plane. A parametric expression of the generating function is obtained for such maps on the projective plane, from which asymptotic evaluations are derived. 相似文献
17.
Chromatic sum equations for rooted cubic planar maps 总被引:4,自引:0,他引:4
Yanpei Liu 《应用数学学报(英文版)》1987,3(2):136-167
This paper provides a functional equation satisfied by rooted nearly cubic planar maps. By a nearly cubic map is meant such a map that all the vertices have valency 3 with the exception of at most the root-vertex. And, as a consequence, the corresponding functional equation for rooted cubic planar maps is found. 相似文献
18.
Roland Rabanal 《Bulletin of the Brazilian Mathematical Society》2010,41(1):73-82
F: ℝ2 → ℝ2 is an almost-area-preserving map if: (a) F is a topological embedding, not necessarily surjective; and (b) there exists a constant s > 0 such that for every measurable set B, μ(F(B)) = sμ(B) where μ is the Lebesgue measure. We study when a differentiable map whose Jacobian determinant is nonzero constant to be
an almost-area-preserving map. In particular, if for all z, the eigenvalues of the Jacobian matrix DF
z
are constant, F is an almost-area-preserving map with convex image. 相似文献
19.
20.
Precise upper bounds are obtained for the minimum weight of minor faces in normal plane maps and 3-polytopes with specified
maximum vertex degree.
Translated fromMatematicheskie Zametki, Vol. 64, No. 5, pp. 648–657, November, 1998.
The research of the first named author was supported in part by the Visiting Fellowship Research Grant GR/K00561 from the
Engineering and Physical Sciences Research Council and by the Russian Foundation for Basic Research under grant No. 96-01-01614
and No. 97-01-01075. 相似文献