Edge-maximal graphs of branchwidth k
نویسندگان
چکیده
In this extended abstract we state some definitions and results from our earlier paper [2] and use these to characterize the class of edge-maximal graphs of branchwidth k. Similarly to the maximal graphs of treewidth k (the k-trees) they turn out to be a subclass of chordal graphs where every minimal separator has size k.
منابع مشابه
Edge-maximal graphs of branchwidth k: The k-branches
Treewidth and branchwidth are two closely related connectivity parameters of graphs. Graphs of treewidth at most k have well-known alternative characterizations as subgraphs of chordal graphs and as partial k-trees. In this paper we give analogous alternative characterizations for graphs of branchwidth at most k. We first show that they are the subgraphs of chordal graphs where every maximal cl...
متن کاملGeneration of Graphs with Bounded Branchwidth
Branchwidth is a connectivity parameter of graphs closely related to treewidth. Graphs of treewidth at most k can be generated algorithmically as the subgraphs of k-trees. In this paper, we investigate the family of edge-maximal graphs of branchwidth k, that we call k-branches. The k-branches are, just as the k-trees, a subclass of the chordal graphs where all minimal separators have size k. Ho...
متن کاملAlgorithmic generation of graphs of branchwidth
Branchwidth is a connectivity parameter of graphs closely related to treewidth. Graphs of treewidth at most k can be generated algorithmically as the subgraphs of k-trees: starting with Kk+1 one repeatedly chooses a k-clique C and adds a new vertex adjacent to vertices in C. In this paper we give an analogous algorithm for generating the graphs of branchwidth at most k. To this end we first inv...
متن کاملBranchwidth of chordal graphs
This paper revisits the ’branchwidth territories’ of Kloks, Kratochv́ıl and Müller [12] to provide a simpler proof and a faster algorithm for computing branchwidth of an interval graph. We also generalize the algorithm to the class of chordal graphs, albeit at the expense of exponential running time. Compliance with the ternary constraint of the branchwidth definition is facilitated by a simple ...
متن کاملOn Total Edge Irregularity Strength of Staircase Graphs and Related Graphs
Let G=(V(G),E(G)) be a connected simple undirected graph with non empty vertex set V(G) and edge set E(G). For a positive integer k, by an edge irregular total k-labeling we mean a function f : V(G)UE(G) --> {1,2,...,k} such that for each two edges ab and cd, it follows that f(a)+f(ab)+f(b) is different from f(c)+f(cd)+f(d), i.e. every two edges have distinct weights. The minimum k for which G ...
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:
- Electronic Notes in Discrete Mathematics
دوره 22 شماره
صفحات -
تاریخ انتشار 2005