Tight toughness bounds for path-factor critical avoidable graphs

Given a graph G and an integer [Formula: see text], a spanning subgraph H of G is called a [Formula: see text]-factor of G if every component of H is a path with at least k vertices. A graph G is [Formula: see text]-factor avoidable if for every edge [Formula: see text], G has a [Formula: see text]-...

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Published inAKCE international journal of graphs and combinatorics Vol. 21; no. 2; pp. 167 - 170
Main Authors Wang, Wenqi, Dai, Guowei
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 03.05.2024
Subjects
05C38
factor critical avoidable graph
Graph
isolated toughness
path-factor
toughness
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Abstract Given a graph G and an integer [Formula: see text], a spanning subgraph H of G is called a [Formula: see text]-factor of G if every component of H is a path with at least k vertices. A graph G is [Formula: see text]-factor avoidable if for every edge [Formula: see text], G has a [Formula: see text]-factor excluding e. A graph G is said to be [Formula: see text]-factor critical avoidable if the graph [Formula: see text] is [Formula: see text]-factor avoidable for any [Formula: see text] with [Formula: see text]. Here we study the sharp bounds of toughness and isolated toughness conditions for the existence of [Formula: see text]-factor critical avoidable graphs. In view of graph theory approaches, this paper mainly contributes to verify that (i) An [Formula: see text]-connected graph is [Formula: see text]-factor critical avoidable if its toughness [Formula: see text]; (ii) An [Formula: see text]-connected graph is [Formula: see text]-factor critical avoidable if its isolated toughness [Formula: see text].
AbstractList Given a graph G and an integer [Formula: see text], a spanning subgraph H of G is called a [Formula: see text]-factor of G if every component of H is a path with at least k vertices. A graph G is [Formula: see text]-factor avoidable if for every edge [Formula: see text], G has a [Formula: see text]-factor excluding e. A graph G is said to be [Formula: see text]-factor critical avoidable if the graph [Formula: see text] is [Formula: see text]-factor avoidable for any [Formula: see text] with [Formula: see text]. Here we study the sharp bounds of toughness and isolated toughness conditions for the existence of [Formula: see text]-factor critical avoidable graphs. In view of graph theory approaches, this paper mainly contributes to verify that (i) An [Formula: see text]-connected graph is [Formula: see text]-factor critical avoidable if its toughness [Formula: see text]; (ii) An [Formula: see text]-connected graph is [Formula: see text]-factor critical avoidable if its isolated toughness [Formula: see text].
Author Wang, Wenqi
Dai, Guowei
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Cites_doi 10.1016/j.disc.2008.04.022
10.7151/dmgt.2353
10.1051/ro/2022208
10.1080/09728600.2022.2094299
10.1007/978-3-540-93952-8
10.1007/s00010-021-00852-4
10.7151/dmgt.2364
10.1002/1097-0118(200104)36:4<175::AID-JGT1005>3.0.CO;2-T
10.1002/jgt.22253
10.4153/CJM-1952-028-2
10.1017/S0004972721000952
10.7151/dmgt.1974
10.7151/dmgt.1426
10.1007/s00373-020-02184-7
10.1016/S0012-365X(01)00214-X
10.1016/0012-365X(73)90138-6
10.1051/ro/2022112
10.1051/ro/2021140
10.1051/ro/2022123
10.1051/ro/2022033
10.1016/S0095-8956(03)00027-3
10.1007/s10255-022-1096-2
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References Bondy J. A. (e_1_3_1_4_1) 1982
Akiyama J. (e_1_3_1_2_1) 2011
Liu H (e_1_3_1_16_1) 2022; 23
e_1_3_1_22_1
e_1_3_1_23_1
e_1_3_1_24_1
e_1_3_1_25_1
e_1_3_1_9_1
e_1_3_1_8_1
e_1_3_1_5_1
e_1_3_1_7_1
e_1_3_1_6_1
e_1_3_1_26_1
e_1_3_1_27_1
e_1_3_1_3_1
e_1_3_1_28_1
Yu Q. (e_1_3_1_21_1) 1987; 2
e_1_3_1_10_1
e_1_3_1_14_1
e_1_3_1_13_1
e_1_3_1_12_1
e_1_3_1_11_1
Yang J. (e_1_3_1_20_1) 2001; 16
e_1_3_1_18_1
e_1_3_1_17_1
e_1_3_1_15_1
e_1_3_1_19_1
References_xml – ident: e_1_3_1_23_1
  doi: 10.1016/j.disc.2008.04.022
– ident: e_1_3_1_8_1
  doi: 10.7151/dmgt.2353
– volume: 23
  start-page: 25
  issue: 1
  year: 2022
  ident: e_1_3_1_16_1
  article-title: Binding number for path-factor uniform graphs
  publication-title: Proc. Romanian Acad. Ser. A: Math. Phys. Techn. Sci. Inf. Sci
  contributor:
    fullname: Liu H
– ident: e_1_3_1_19_1
  doi: 10.1051/ro/2022208
– ident: e_1_3_1_5_1
  doi: 10.1080/09728600.2022.2094299
– ident: e_1_3_1_22_1
  doi: 10.1007/978-3-540-93952-8
– ident: e_1_3_1_26_1
  doi: 10.1007/s00010-021-00852-4
– ident: e_1_3_1_25_1
  doi: 10.7151/dmgt.2364
– ident: e_1_3_1_13_1
  doi: 10.1002/1097-0118(200104)36:4<175::AID-JGT1005>3.0.CO;2-T
– ident: e_1_3_1_12_1
  doi: 10.1002/jgt.22253
– ident: e_1_3_1_17_1
  doi: 10.4153/CJM-1952-028-2
– ident: e_1_3_1_27_1
  doi: 10.1017/S0004972721000952
– ident: e_1_3_1_28_1
  doi: 10.7151/dmgt.1974
– ident: e_1_3_1_15_1
  doi: 10.7151/dmgt.1426
– start-page: 1
  volume-title: Lecture Notes in Mathematics
  year: 2011
  ident: e_1_3_1_2_1
  contributor:
    fullname: Akiyama J.
– volume: 2
  start-page: 211
  year: 1987
  ident: e_1_3_1_21_1
  article-title: On tree-factor covered graphs
  publication-title: J. Combin. Math. Combin. Comput
  contributor:
    fullname: Yu Q.
– ident: e_1_3_1_10_1
  doi: 10.1007/s00373-020-02184-7
– ident: e_1_3_1_3_1
  doi: 10.1016/S0012-365X(01)00214-X
– volume-title: Graph Theory with Applications
  year: 1982
  ident: e_1_3_1_4_1
  contributor:
    fullname: Bondy J. A.
– ident: e_1_3_1_6_1
  doi: 10.1016/0012-365X(73)90138-6
– volume: 16
  start-page: 385
  year: 2001
  ident: e_1_3_1_20_1
  article-title: Fractional (g, f)-factors in graphs
  publication-title: Appl. Math. J. Chinese Univ. Ser. A
  contributor:
    fullname: Yang J.
– ident: e_1_3_1_9_1
  doi: 10.1051/ro/2022112
– ident: e_1_3_1_11_1
  doi: 10.1051/ro/2021140
– ident: e_1_3_1_18_1
  doi: 10.1051/ro/2022123
– ident: e_1_3_1_7_1
  doi: 10.1051/ro/2022033
– ident: e_1_3_1_14_1
  doi: 10.1016/S0095-8956(03)00027-3
– ident: e_1_3_1_24_1
  doi: 10.1007/s10255-022-1096-2
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SubjectTerms 05C38
factor critical avoidable graph
Graph
isolated toughness
path-factor
toughness
Title Tight toughness bounds for path-factor critical avoidable graphs
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