# Matchings and total domination subdivision number in graphs with few induced 4-cycles

Odile Favaron; Hossein Karami; Rana Khoeilar; Seyed Mahmoud Sheikholeslami

Discussiones Mathematicae Graph Theory (2010)

- Volume: 30, Issue: 4, page 611-618
- ISSN: 2083-5892

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topOdile Favaron, et al. "Matchings and total domination subdivision number in graphs with few induced 4-cycles." Discussiones Mathematicae Graph Theory 30.4 (2010): 611-618. <http://eudml.org/doc/270987>.

@article{OdileFavaron2010,

abstract = {A set S of vertices of a graph G = (V,E) without isolated vertex is a total dominating set if every vertex of V(G) is adjacent to some vertex in S. The total domination number γₜ(G) is the minimum cardinality of a total dominating set of G. The total domination subdivision number $sd_\{γₜ(G)\}$ is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the total domination number. Favaron, Karami, Khoeilar and Sheikholeslami (Journal of Combinatorial Optimization, to appear) conjectured that: For any connected graph G of order n ≥ 3, $sd_\{γₜ(G)\} ≤ γₜ(G)+1$. In this paper we use matchings to prove this conjecture for graphs with at most three induced 4-cycles through each vertex.},

author = {Odile Favaron, Hossein Karami, Rana Khoeilar, Seyed Mahmoud Sheikholeslami},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {matching; barrier; total domination number; total domination subdivision number},

language = {eng},

number = {4},

pages = {611-618},

title = {Matchings and total domination subdivision number in graphs with few induced 4-cycles},

url = {http://eudml.org/doc/270987},

volume = {30},

year = {2010},

}

TY - JOUR

AU - Odile Favaron

AU - Hossein Karami

AU - Rana Khoeilar

AU - Seyed Mahmoud Sheikholeslami

TI - Matchings and total domination subdivision number in graphs with few induced 4-cycles

JO - Discussiones Mathematicae Graph Theory

PY - 2010

VL - 30

IS - 4

SP - 611

EP - 618

AB - A set S of vertices of a graph G = (V,E) without isolated vertex is a total dominating set if every vertex of V(G) is adjacent to some vertex in S. The total domination number γₜ(G) is the minimum cardinality of a total dominating set of G. The total domination subdivision number $sd_{γₜ(G)}$ is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the total domination number. Favaron, Karami, Khoeilar and Sheikholeslami (Journal of Combinatorial Optimization, to appear) conjectured that: For any connected graph G of order n ≥ 3, $sd_{γₜ(G)} ≤ γₜ(G)+1$. In this paper we use matchings to prove this conjecture for graphs with at most three induced 4-cycles through each vertex.

LA - eng

KW - matching; barrier; total domination number; total domination subdivision number

UR - http://eudml.org/doc/270987

ER -

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