Forbidden subgraphs for collapsible graphs and supereulerian graphs

Supereulerian graphs with width s and s-collapsible graphs

Discrete Applied Mathematics ◽

10.1016/j.dam.2015.07.013 ◽

2016 ◽

Vol 200 ◽

pp. 79-94 ◽

Cited By ~ 5

Author(s):

Ping Li ◽

Hao Li ◽

Ye Chen ◽

Herbert Fleischner ◽

Hong-Jian Lai

Keyword(s):

Supereulerian Graphs ◽

Collapsible Graphs

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Pairs of forbidden subgraphs and 2-connected supereulerian graphs

Discrete Mathematics ◽

10.1016/j.disc.2018.03.009 ◽

2018 ◽

Vol 341 (6) ◽

pp. 1696-1707 ◽

Cited By ~ 2

Author(s):

Roman Čada ◽

Kenta Ozeki ◽

Liming Xiong ◽

Kiyoshi Yoshimoto

Keyword(s):

Forbidden Subgraphs ◽

Supereulerian Graphs

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Toughness, Forbidden Subgraphs and Pancyclicity

Graphs and Combinatorics ◽

10.1007/s00373-021-02284-y ◽

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.

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Forbidden subgraphs of graphs uniquely Hamiltonian-connected from a vertex

Discrete Mathematics ◽

10.1016/s0012-365x(97)00220-3 ◽

1998 ◽

Vol 187 (1-3) ◽

pp. 281-290 ◽

Cited By ~ 1

Author(s):

George R.T. Hendry ◽

C.J. Knickerbocker ◽

Patti Frazer Lock ◽

Michael Sheard

Keyword(s):

Forbidden Subgraphs ◽

Hamiltonian Connected

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The supereulerian graphs in the graph family C(l,k)

Discrete Mathematics ◽

10.1016/j.disc.2008.06.038 ◽

2009 ◽

Vol 309 (9) ◽

pp. 2937-2942 ◽

Cited By ~ 8

Author(s):

Xiaomin Li ◽

Dengxin Li ◽

Hong-Jian Lai

Keyword(s):

Supereulerian Graphs

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

Algorithms ◽

10.3390/a14040105 ◽

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.

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