Complexity of Disjoint Π-Vertex Deletion for Disconnected Forbidden Subgraphs

2014 ◽  
pp. 286-297
Author(s):  
Jiong Guo ◽  
Yash Raj Shrestha
Keyword(s):  
Forbidden Subgraphs ◽  
Vertex Deletion

scholarly journals Complexity of Disjoint Π-Vertex Deletion for Disconnected Forbidden Subgraphs

2014 ◽  
Vol 18 (4) ◽  
pp. 603-631 ◽  
Author(s):  
Jiong Guo ◽  
Yash Raj Shrestha
Keyword(s):  
Forbidden Subgraphs ◽  
Vertex Deletion

Vertex deletion and cycles in multipartite tournaments

1999 ◽  
Vol 197-198 (1-3) ◽  
pp. 769-779 ◽  
Author(s):  
M Tewes
Keyword(s):  
Multipartite Tournaments ◽  
Vertex Deletion

scholarly journals A Polynomial Kernel for Distance-Hereditary Vertex Deletion

Algorithmica ◽  
2021 ◽  
Author(s):  
Eun Jung Kim ◽  
O-joung Kwon
Keyword(s):  
Polynomial Kernel ◽  
Vertex Deletion

scholarly journals Toughness, Forbidden Subgraphs and Pancyclicity

2021 ◽  
Vol 37 (3) ◽  
pp. 839-866
Author(s):  
Wei Zheng ◽  
Hajo Broersma ◽  
Ligong Wang
Keyword(s):  
Recent Article ◽  
Forbidden Subgraph ◽  
Forbidden Subgraphs ◽  
Free Graph ◽  
Induced Subgraph ◽  
Complete Answer ◽  
Open Case

AbstractMotivated by several conjectures due to Nikoghosyan, in a recent article due to Li et al., the aim was to characterize all possible graphs H such that every 1-tough H-free graph is hamiltonian. The almost complete answer was given there by the conclusion that every proper induced subgraph H of $$K_1\cup P_4$$ K 1 ∪ P 4 can act as a forbidden subgraph to ensure that every 1-tough H-free graph is hamiltonian, and that there is no other forbidden subgraph with this property, except possibly for the graph $$K_1\cup P_4$$ K 1 ∪ P 4 itself. The hamiltonicity of 1-tough $$K_1\cup P_4$$ K 1 ∪ P 4 -free graphs, as conjectured by Nikoghosyan, was left there as an open case. In this paper, we consider the stronger property of pancyclicity under the same condition. We find that the results are completely analogous to the hamiltonian case: every graph H such that any 1-tough H-free graph is hamiltonian also ensures that every 1-tough H-free graph is pancyclic, except for a few specific classes of graphs. Moreover, there is no other forbidden subgraph having this property. With respect to the open case for hamiltonicity of 1-tough $$K_1\cup P_4$$ K 1 ∪ P 4 -free graphs we give infinite families of graphs that are not pancyclic.

scholarly journals Vertex deletion parameterized by elimination distance and even less

2021 ◽  
Author(s):  
Bart M. P. Jansen ◽  
Jari J. H. de Kroon ◽  
Michał Włodarczyk
Keyword(s):  
Vertex Deletion

scholarly journals Forbidden subgraphs of graphs uniquely Hamiltonian-connected from a vertex

1998 ◽  
Vol 187 (1-3) ◽  
pp. 281-290 ◽  
Author(s):  
George R.T. Hendry ◽  
C.J. Knickerbocker ◽  
Patti Frazer Lock ◽  
Michael Sheard
Keyword(s):  
Forbidden Subgraphs ◽  
Hamiltonian Connected

scholarly journals A Quasi-Hole Detection Algorithm for Recognizing k-Distance-Hereditary Graphs, with k < 2

Algorithms ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 105
Author(s):  
Serafino Cicerone
Keyword(s):  
Polynomial Time ◽  
Detection Algorithm ◽  
Recognition Algorithm ◽  
Forbidden Subgraphs ◽  
Induced Subgraph ◽  
Hole Detection

Cicerone and Di Stefano defined and studied the class of k-distance-hereditary graphs, i.e., graphs where the distance in each connected induced subgraph is at most k times the distance in the whole graph. The defined graphs represent a generalization of the well known distance-hereditary graphs, which actually correspond to 1-distance-hereditary graphs. In this paper we make a step forward in the study of these new graphs by providing characterizations for the class of all the k-distance-hereditary graphs such that k<2. The new characterizations are given in terms of both forbidden subgraphs and cycle-chord properties. Such results also lead to devise a polynomial-time recognition algorithm for this kind of graph that, according to the provided characterizations, simply detects the presence of quasi-holes in any given graph.

scholarly journals Feedback Vertex Set Inspired Kernel for Chordal Vertex Deletion

2019 ◽  
Vol 15 (1) ◽  
pp. 1-28 ◽  
Author(s):  
Akanksha Agrawal ◽  
Daniel Lokshtanov ◽  
Pranabendu Misra ◽  
Saket Saurabh ◽  
Meirav Zehavi
Keyword(s):  
Feedback Vertex Set ◽  
Vertex Deletion ◽  
Vertex Set

scholarly journals Three-colourability and forbidden subgraphs. II: polynomial algorithms

2002 ◽  
Vol 251 (1-3) ◽  
pp. 137-153 ◽  
Author(s):  
Bert Randerath ◽  
Ingo Schiermeyer ◽  
Meike Tewes
Keyword(s):  
Polynomial Algorithms ◽  
Forbidden Subgraphs

Clique-Width for Four-Vertex Forbidden Subgraphs

2005 ◽  
pp. 185-196
Author(s):  
Andreas Brandstädt ◽  
Joost Engelfriet ◽  
Hoàng-Oanh Le ◽  
Vadim V. Lozin
Keyword(s):  
Forbidden Subgraphs
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