Quadrangular embeddings of complete graphs and the Even Map Color Theorem
نویسندگان
چکیده
منابع مشابه
Quadrangular embeddings of complete graphs∗
Hartsfield and Ringel proved that a complete graph Kn has an orientable quadrangular embedding if n ≡ 5 (mod 8), and has a nonorientable quadrangular embedding if n ≥ 9 and n ≡ 1 (mod 4). We complete the characterization of complete graphs admitting quadrangular embeddings by showing that Kn has an orientable quadrilateral embedding if n ≡ 0 (mod 8), and has a nonorientable quadrilateral embedd...
متن کاملLabeling Subgraph Embeddings and Cordiality of Graphs
Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$, a vertex labeling $f : V(G)rightarrow mathbb{Z}_2$ induces an edge labeling $ f^{+} : E(G)rightarrow mathbb{Z}_2$ defined by $f^{+}(xy) = f(x) + f(y)$, for each edge $ xyin E(G)$. For each $i in mathbb{Z}_2$, let $ v_{f}(i)=|{u in V(G) : f(u) = i}|$ and $e_{f^+}(i)=|{xyin E(G) : f^{+}(xy) = i}|$. A vertex labeling $f$ of a graph $G...
متن کاملTriangular embeddings of complete graphs
In this paper we describe the generation of all nonorientable triangular embeddings of the complete graphs K12 and K13. (The 59 nonisomorphic orientable triangular embeddings of K12 were found in 1996 by Altshuler, Bokowski and Schuchert, and K13 has no orientable triangular embeddings.) There are 182, 200 nonisomorphic nonorientable triangular embeddings for K12, and 243, 088, 286 for K13. Tri...
متن کاملReformulating the map color theorem
This paper discusses reformulations of the problem of coloring plane maps with four colors. We include discussion of the Eliahou-Kryuchkov conjecture, the Penrose formula, the vector cross product formulation and the reformulations in terms of formations and factorizations due to G. Spencer-Brown.
متن کاملMETA-HEURISTIC ALGORITHMS FOR MINIMIZING THE NUMBER OF CROSSING OF COMPLETE GRAPHS AND COMPLETE BIPARTITE GRAPHS
The minimum crossing number problem is among the oldest and most fundamental problems arising in the area of automatic graph drawing. In this paper, eight population-based meta-heuristic algorithms are utilized to tackle the minimum crossing number problem for two special types of graphs, namely complete graphs and complete bipartite graphs. A 2-page book drawing representation is employed for ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2019
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2019.02.006