A Neighborhood Condition for Fractional ID-[A, B]-Factor-Critical Graphs

Sizhong Zhou; Fan Yang; Zhiren Sun

Discussiones Mathematicae Graph Theory (2016)

  • Volume: 36, Issue: 2, page 409-418
  • ISSN: 2083-5892

Abstract

top
Let G be a graph of order n, and let a and b be two integers with 1 ≤ a ≤ b. Let h : E(G) → [0, 1] be a function. If a ≤ ∑e∋x h(e) ≤ b holds for any x ∈ V (G), then we call G[Fh] a fractional [a, b]-factor of G with indicator function h, where Fh = {e ∈ E(G) : h(e) > 0}. A graph G is fractional independent-set-deletable [a, b]-factor-critical (in short, fractional ID-[a, b]- factor-critical) if G − I has a fractional [a, b]-factor for every independent set I of G. In this paper, it is proved that if [...] for any two nonadjacent vertices x, y ∈ V (G), then G is fractional ID-[a, b]-factor-critical. Furthermore, it is shown that this result is best possible in some sense.

How to cite

top

Sizhong Zhou, Fan Yang, and Zhiren Sun. "A Neighborhood Condition for Fractional ID-[A, B]-Factor-Critical Graphs." Discussiones Mathematicae Graph Theory 36.2 (2016): 409-418. <http://eudml.org/doc/277129>.

@article{SizhongZhou2016,
abstract = {Let G be a graph of order n, and let a and b be two integers with 1 ≤ a ≤ b. Let h : E(G) → [0, 1] be a function. If a ≤ ∑e∋x h(e) ≤ b holds for any x ∈ V (G), then we call G[Fh] a fractional [a, b]-factor of G with indicator function h, where Fh = \{e ∈ E(G) : h(e) > 0\}. A graph G is fractional independent-set-deletable [a, b]-factor-critical (in short, fractional ID-[a, b]- factor-critical) if G − I has a fractional [a, b]-factor for every independent set I of G. In this paper, it is proved that if [...] for any two nonadjacent vertices x, y ∈ V (G), then G is fractional ID-[a, b]-factor-critical. Furthermore, it is shown that this result is best possible in some sense.},
author = {Sizhong Zhou, Fan Yang, Zhiren Sun},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {graph; minimum degree; neighborhood; fractional [a; b]-factor; fractional ID-[a; b]-factor-critical graph; fractional -factor; fractional ID--factor-critical graph},
language = {eng},
number = {2},
pages = {409-418},
title = {A Neighborhood Condition for Fractional ID-[A, B]-Factor-Critical Graphs},
url = {http://eudml.org/doc/277129},
volume = {36},
year = {2016},
}

TY - JOUR
AU - Sizhong Zhou
AU - Fan Yang
AU - Zhiren Sun
TI - A Neighborhood Condition for Fractional ID-[A, B]-Factor-Critical Graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2016
VL - 36
IS - 2
SP - 409
EP - 418
AB - Let G be a graph of order n, and let a and b be two integers with 1 ≤ a ≤ b. Let h : E(G) → [0, 1] be a function. If a ≤ ∑e∋x h(e) ≤ b holds for any x ∈ V (G), then we call G[Fh] a fractional [a, b]-factor of G with indicator function h, where Fh = {e ∈ E(G) : h(e) > 0}. A graph G is fractional independent-set-deletable [a, b]-factor-critical (in short, fractional ID-[a, b]- factor-critical) if G − I has a fractional [a, b]-factor for every independent set I of G. In this paper, it is proved that if [...] for any two nonadjacent vertices x, y ∈ V (G), then G is fractional ID-[a, b]-factor-critical. Furthermore, it is shown that this result is best possible in some sense.
LA - eng
KW - graph; minimum degree; neighborhood; fractional [a; b]-factor; fractional ID-[a; b]-factor-critical graph; fractional -factor; fractional ID--factor-critical graph
UR - http://eudml.org/doc/277129
ER -

References

top
  1. [1] S. Zhou, Z. Sun and H. Liu, A minimum degree condition for fractional ID-[a, b]- factor-critical graphs, Bull. Aust. Math. Soc. 86 (2012) 177-183. doi:10.1017/S0004972711003467[Crossref][WoS] Zbl1252.05182
  2. [2] H. Matsuda, A neighborhood condition for graphs to have [a, b]-factors, Discrete Math. 224 (2000) 289-292. doi:10.1016/S0012-365X(00)00140-0[Crossref] Zbl0966.05062
  3. [3] J. Ekstein, P. Holub, T. Kaiser, L. Xiong and S. Zhang, Star subdivisions and con- nected even factors in the square of a graph, Discrete Math. 312 (2012) 2574-2578. doi:10.1016/j.disc.2011.09.004[Crossref][WoS] Zbl1246.05095
  4. [4] H. Lu, Simplified existence theorems on all fractional [a, b]-factors, Discrete Appl. Math. 161 (2013) 2075-2078. doi:10.1016/j.dam.2013.02.006[Crossref] 
  5. [5] S. Zhou, Independence number, connectivity and (a, b, k)-critical graphs, Discrete Math. 309 (2009) 4144-4148. doi:10.1016/j.disc.2008.12.013[Crossref][WoS] 
  6. [6] S. Zhou, A sufficient condition for graphs to be fractional (k,m)-deleted graphs, Appl. Math. Lett. 24 (2011) 1533-1538. doi:10.1016/j.aml.2011.03.041[WoS][Crossref] 
  7. [7] S. Zhou and H. Liu, Neighborhood conditions and fractional k-factors, Bull. Malays. Math. Sci. Soc. 32 (2009) 37-45. Zbl1209.05196
  8. [8] K. Kimura, f-factors, complete-factors, and component-deleted subgraphs, Discrete Math. 313 (2013) 1452-1463. doi:10.1016/j.disc.2013.03.009[Crossref][WoS] Zbl1279.05056
  9. [9] M. Kouider and Z. Lonc, Stability number and [a, b]-factors in graphs, J. Graph Theory 46 (2004) 254-264. doi:10.1002/jgt.20008[Crossref] 
  10. [10] R. Chang, G. Liu and Y. Zhu, Degree conditions of fractional ID-k-factor-critical graphs, Bull. Malays. Math. Sci. Soc. 33 (2010) 355-360. Zbl1260.05119
  11. [11] S. Zhou, Q. Bian and J. Wu, A result on fractional ID-k-factor-critical graphs, J. Combin. Math. Combin. Comput. 87 (2013) 229-236. Zbl1293.05310
  12. [12] S. Zhou, Binding numbers for fractional ID-k-factor-critical graphs, Acta Math. Sin. Engl. Ser. 30 (2014) 181-186. doi:10.1007/s10114-013-1396-9[Crossref][WoS] Zbl1287.05124
  13. [13] G. Liu and L. Zhang, Fractional (g, f)-factors of graphs, Acta Math. Sci. Ser. B 21 (2001) 541-545. Zbl0989.05086

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.