General Lower Bounds for the Minor Crossing Number of Graphs
نویسندگان
چکیده
There are three general lower bound techniques for the crossing numbers of graphs: the Crossing Lemma, the bisection method and the embedding method. In this contribution, we present their adaptations to the minor crossing number. Using the adapted bounds, we improve on the known bounds on the minor crossing number of hypercubes. We also point out relations of the minor crossing number to string graphs.
منابع مشابه
Some lower bounds for the $L$-intersection number of graphs
For a set of non-negative integers~$L$, the $L$-intersection number of a graph is the smallest number~$l$ for which there is an assignment of subsets $A_v subseteq {1,dots, l}$ to vertices $v$, such that every two vertices $u,v$ are adjacent if and only if $|A_u cap A_v|in L$. The bipartite $L$-intersection number is defined similarly when the conditions are considered only for the ver...
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 کاملGraph minors and the crossing number of graphs
There are three general lower bound techniques for the crossing numbers of graphs, all of which can be traced back to Leighton’s work on applications of crossing number in VLSI: the Crossing Lemma, the Bisection Method, and the Embedding Method. In this contribution, we sketch their adaptations to the minor crossing number.
متن کاملBiplanar Crossing Numbers I: A Survey of Results and Problems
We survey known results and propose open problems on the biplanar crossing number. We study biplanar crossing numbers of speci c families of graphs, in particular, of complete bipartite graphs. We nd a few particular exact values and give general lower and upper bounds for the biplanar crossing number. We nd the exact biplanar crossing number of K5;q for every q.
متن کاملThe minus k-domination numbers in graphs
For any integer , a minus k-dominating function is afunction f : V (G) {-1,0, 1} satisfying w) for every vertex v, where N(v) ={u V(G) | uv E(G)} and N[v] =N(v)cup {v}. The minimum of the values of v), taken over all minusk-dominating functions f, is called the minus k-dominationnumber and is denoted by $gamma_k^-(G)$ . In this paper, we introduce the study of minu...
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 & Computational Geometry
دوره 44 شماره
صفحات -
تاریخ انتشار 2010