A Quasi-Hole Detection Algorithm for Recognizing k-Distance-Hereditary Graphs, with k < 2
نویسندگان
چکیده
Cicerone and Di Stefano defined studied the class of k-distance-hereditary graphs, i.e., graphs where distance in each connected induced subgraph is at most k times whole graph. The represent a generalization well known distance-hereditary which actually correspond to 1-distance-hereditary graphs. In this paper we make step forward study these new by providing characterizations for all such that k<2. are given terms both forbidden subgraphs cycle-chord properties. Such results also lead devise polynomial-time recognition algorithm kind graph that, according provided characterizations, simply detects presence quasi-holes any
منابع مشابه
(k, +)-Distance-Hereditary Graphs
In this work we introduce, characterize, and provide algorithmic results for (k, +)–distance-hereditary graphs, k ≥ 0. These graphs can be used to model interconnection networks with desirable connectivity properties; a network modeled as a (k, +)–distance-hereditary graph can be characterized as follows: if some nodes have failed, as long as two nodes remain connected, the distance between the...
متن کاملRecognizing k-path Graphs
The k-path graph Pk(H) of a graph H has all length-k paths of H as vertices; two such vertices are adjacent in the new graph if their union forms a path or cycle of length k + 1 in H , and if the common edges of both paths form a path of length k − 1. In this paper we give a (nonpolynomial) recognition algorithm for k-path graphs, for every integer k¿2. The algorithm runs in polynomial time if ...
متن کاملk-Quasi-Planar Graphs
A topological graph is k-quasi-planar if it does not contain k pairwise crossing edges. A topological graph is simple if every pair of its edges intersect at most once (either at a vertex or at their intersection). In 1996, Pach, Shahrokhi, and Szegedy [16] showed that every n-vertex simple k-quasi-planar graph contains at most O ( n(logn) ) edges. This upper bound was recently improved (for la...
متن کاملtotal $k$-distance domination critical graphs
a set $s$ of vertices in a graph $g=(v,e)$ is called a total$k$-distance dominating set if every vertex in $v$ is withindistance $k$ of a vertex in $s$. a graph $g$ is total $k$-distancedomination-critical if $gamma_{t}^{k} (g - x) < gamma_{t}^{k}(g)$ for any vertex $xin v(g)$. in this paper,we investigate some results on total $k$-distance domination-critical of graphs.
متن کاملWeighted connected k-domination and weighted k-dominating clique in distance-hereditary graphs
A graph is distance-hereditary if the distance between any two vertices in a connected induced subgraph is the same as in the original graph. This paper presents e-cient algorithms for solving the weighted connected k-domination and the weighted k-dominating clique problems in distance-hereditary graphs. c © 2001 Elsevier Science B.V. All rights reserved.
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: Algorithms
سال: 2021
ISSN: ['1999-4893']
DOI: https://doi.org/10.3390/a14040105