Finding Intersection Models of Weakly Chordal Graphs

2006 ◽  
pp. 241-255 ◽  
Author(s):  
Martin Charles Golumbic ◽  
Marina Lipshteyn ◽  
Michal Stern
Keyword(s):  
Chordal Graphs

Chordal graphs

2021 ◽  
pp. 130-151
Author(s):  
Martin Charles Golumbic
Keyword(s):  
Chordal Graphs

On 3-Degree 4-Chordal Graphs

2020 ◽  
Author(s):  
Devarshi Aggarwal ◽  
R.Mahendra Kumar ◽  
Shwet Prakash ◽  
N. Sadagopan
Keyword(s):  
Chordal Graphs

k-Efficient domination: Algorithmic perspective

2022 ◽  
Author(s):  
Mohsen Alambardar Meybodi
Keyword(s):  
Decision Problem ◽  
Dominating Set ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Chordal Graphs ◽  
Sparse Graphs ◽  
Fpt Algorithm ◽  
Domination Problem ◽  
Efficient Dominating Set ◽  
Np Complete

A set [Formula: see text] of a graph [Formula: see text] is called an efficient dominating set of [Formula: see text] if every vertex [Formula: see text] has exactly one neighbor in [Formula: see text], in other words, the vertex set [Formula: see text] is partitioned to some circles with radius one such that the vertices in [Formula: see text] are the centers of partitions. A generalization of this concept, introduced by Chellali et al. [k-Efficient partitions of graphs, Commun. Comb. Optim. 4 (2019) 109–122], is called [Formula: see text]-efficient dominating set that briefly partitions the vertices of graph with different radiuses. It leads to a partition set [Formula: see text] such that each [Formula: see text] consists a center vertex [Formula: see text] and all the vertices in distance [Formula: see text], where [Formula: see text]. In other words, there exist the dominators with various dominating powers. The problem of finding minimum set [Formula: see text] is called the minimum [Formula: see text]-efficient domination problem. Given a positive integer [Formula: see text] and a graph [Formula: see text], the [Formula: see text]-efficient Domination Decision problem is to decide whether [Formula: see text] has a [Formula: see text]-efficient dominating set of cardinality at most [Formula: see text]. The [Formula: see text]-efficient Domination Decision problem is known to be NP-complete even for bipartite graphs [M. Chellali, T. W. Haynes and S. Hedetniemi, k-Efficient partitions of graphs, Commun. Comb. Optim. 4 (2019) 109–122]. Clearly, every graph has a [Formula: see text]-efficient dominating set but it is not correct for efficient dominating set. In this paper, we study the following: [Formula: see text]-efficient domination problem set is NP-complete even in chordal graphs. A polynomial-time algorithm for [Formula: see text]-efficient domination in trees. [Formula: see text]-efficient domination on sparse graphs from the parametrized complexity perspective. In particular, we show that it is [Formula: see text]-hard on d-degenerate graphs while the original dominating set has Fixed Parameter Tractable (FPT) algorithm on d-degenerate graphs. [Formula: see text]-efficient domination on nowhere-dense graphs is FPT.

Dually Chordal Graphs

1998 ◽  
Vol 11 (3) ◽  
pp. 437-455 ◽  
Author(s):  
Andreas Brandstädt ◽  
Feodor Dragan ◽  
Victor Chepoi ◽  
Vitaly Voloshin
Keyword(s):  
Chordal Graphs

scholarly journals $b$-vectors of chordal graphs

2020 ◽  
Vol 12 (4) ◽  
pp. 539-557
Author(s):  
Luis Pedro Montejano ◽  
Luis Núñez-Betancourt
Keyword(s):  
Chordal Graphs

scholarly journals Graph isomorphism completeness for chordal bipartite graphs and strongly chordal graphs

2005 ◽  
Vol 145 (3) ◽  
pp. 479-482 ◽  
Author(s):  
Ryuhei Uehara ◽  
Seinosuke Toda ◽  
Takayuki Nagoya
Keyword(s):  
Graph Isomorphism ◽  
Bipartite Graphs ◽  
Chordal Graphs ◽  
Strongly Chordal Graphs ◽  
Chordal Bipartite Graphs

scholarly journals Eccentricity-approximating trees in chordal graphs

2000 ◽  
Vol 220 (1-3) ◽  
pp. 263-269 ◽  
Author(s):  
Erich Prisner
Keyword(s):  
Chordal Graphs
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