The pagenumber of toroidal graphs is at most seven
نویسنده
چکیده
In this paper, we show that seven pages are sufficient for a book embedding of any toroidal graph.
منابع مشابه
On list vertex 2-arboricity of toroidal graphs without cycles of specific length
The vertex arboricity $rho(G)$ of a graph $G$ is the minimum number of subsets into which the vertex set $V(G)$ can be partitioned so that each subset induces an acyclic graph. A graph $G$ is called list vertex $k$-arborable if for any set $L(v)$ of cardinality at least $k$ at each vertex $v$ of $G$, one can choose a color for each $v$ from its list $L(v)$ so that the subgraph induced by ev...
متن کاملEmbedding Planar Graphs in Seven Pages
This paper investigates the problem of embedding planar graphs in books of few pages. An efficient algorithm for embedding a planar graph in a book establishes an upper bound of seven pages for any planar graph. This disproves a conjecture of Bernhart and Kainen that the pagenumber of a planar graph can be arbitrarily large. I t is also shown that the stellations of K3 have pagenumber three, th...
متن کاملMinimum Tenacity of Toroidal graphs
The tenacity of a graph G, T(G), is dened by T(G) = min{[|S|+τ(G-S)]/[ω(G-S)]}, where the minimum is taken over all vertex cutsets S of G. We dene τ(G - S) to be the number of the vertices in the largest component of the graph G - S, and ω(G - S) be the number of components of G - S.In this paper a lower bound for the tenacity T(G) of a graph with genus γ(G) is obtained using the graph's connec...
متن کاملOn independent domination numbers of grid and toroidal grid directed graphs
A subset $S$ of vertex set $V(D)$ is an {em indpendent dominating set} of $D$ if $S$ is both an independent and a dominating set of $D$. The {em indpendent domination number}, $i(D)$ is the cardinality of the smallest independent dominating set of $D$. In this paper we calculate the independent domination number of the { em cartesian product} of two {em directed paths} $P_m$ and $P_n$ for arbi...
متن کاملMatching Integral Graphs of Small Order
In this paper, we study matching integral graphs of small order. A graph is called matching integral if the zeros of its matching polynomial are all integers. Matching integral graphs were first studied by Akbari, Khalashi, etc. They characterized all traceable graphs which are matching integral. They studied matching integral regular graphs. Furthermore, it has been shown that there is no matc...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Discrete Mathematics
دوره 175 شماره
صفحات -
تاریخ انتشار 1997