On matching extendability of lexicographic products

2017 ◽  
Vol 51 (3) ◽  
pp. 857-873 ◽  
Author(s):  
Nina Chiarelli ◽  
Cemil Dibek ◽  
Tınaz Ekim ◽  
Didem Gözüpek ◽  
Štefko Miklavič
Keyword(s):  
Matching Extendability

Distance-restricted matching extendability of fullerene graphs

2017 ◽  
Vol 56 (2) ◽  
pp. 606-617
Author(s):  
Michitaka Furuya ◽  
Masanori Takatou ◽  
Shoichi Tsuchiya
Keyword(s):  
Matching Extendability ◽  
Fullerene Graphs

scholarly journals On the matching extendability of graphs in surfaces

2008 ◽  
Vol 98 (1) ◽  
pp. 105-115 ◽  
Author(s):  
R.E.L. Aldred ◽  
Ken-ichi Kawarabayashi ◽  
Michael D. Plummer
Keyword(s):  
Matching Extendability

K − Bipartite Matching Extendability of Special Graphs

2011 ◽  
Vol 121-126 ◽  
pp. 4008-4012
Author(s):  
Zhi Hao Hui ◽  
Jin Wei Yang ◽  
Biao Zhao
Keyword(s):  
Positive Integer ◽  
Connected Graph ◽  
Perfect Matching ◽  
Bipartite Matching ◽  
Simple Connected Graph ◽  
Matching Extendability

Let be a simple connected graph containing a perfect matching. For a positive integer , , is said to be bipartite matching extendable if every bipartite matching of with is included in a perfect matching of . In this paper, we show that bipartite matching extendability of some special graphs.

The Matching Extendability of Optimal 1-Planar Graphs

2018 ◽  
Vol 34 (5) ◽  
pp. 1089-1099 ◽  
Author(s):  
Jun Fujisawa ◽  
Keita Segawa ◽  
Yusuke Suzuki
Keyword(s):  
Planar Graphs ◽  
Matching Extendability

scholarly journals Matching Extendabilities of G = Cm ∨ Pn

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 941 ◽  
Author(s):  
Zhi-hao Hui ◽  
Yu Yang ◽  
Hua Wang ◽  
Xiao-jun Sun
Keyword(s):  
Perfect Matching ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Bipartite Matching ◽  
Induced Matching ◽  
Necessary And Sufficient ◽  
Graph Join ◽  
Matching Extendability

A graph is considered to be induced-matching extendable (bipartite matching extendable) if every induced matching (bipartite matching) of G is included in a perfect matching of G. The induced-matching extendability and bipartite-matching extendability of graphs have been of interest. By letting G = C m ∨ P n ( m ≥ 3 and n ≥ 1 ) be the graph join of C m (the cycle with m vertices) and P n (the path with n vertices) contains a perfect matching, we find necessary and sufficient conditions for G to be induced-matching extendable and bipartite-matching extendable.

Towards a problem of Ruskey and Savage on matching extendability

2017 ◽  
Vol 61 ◽  
pp. 437-443
Author(s):  
Jiří Fink ◽  
Tomáš Dvořák ◽  
Petr Gregor ◽  
Tomáš Novotný
Keyword(s):  
Matching Extendability

Forbidden pairs for the matching extendability of graphs with connectivity at least 2 or 3

2020 ◽  
Vol 343 (4) ◽  
pp. 111694
Author(s):  
Zhihao Hui ◽  
Junfeng Du ◽  
Shipeng Wang ◽  
Liming Xiong ◽  
Xiaojing Yang
Keyword(s):  
Matching Extendability

BIPARTITE MATCHING EXTENDABILITY AND TOUGHNESS

2010 ◽  
Vol 02 (01) ◽  
pp. 33-44
Author(s):  
XIUMEI WANG ◽  
SUJING ZHOU ◽  
YIXUN LIN
Keyword(s):  
Perfect Matching ◽  
Necessary Conditions ◽  
Simple Graph ◽  
Sufficient Condition ◽  
Bipartite Matching ◽  
Bipartite Subgraph ◽  
Matching Extendability

Let G be a simple graph containing a perfect matching. G is said to be bipartite matching extendable (BM-extendable) if every matching M which is a perfect matching of an induced bipartite subgraph extends to a perfect matching of G. In this paper, we study some relations between toughness and BM-extendability of a graph, including some sufficient or necessary conditions about toughness for a graph to be BM-extendable, and a sufficient condition for a BM-extendable graph to be 1-tough.

scholarly journals Extending a perfect matching to a Hamiltonian cycle

2015 ◽  
Vol Vol. 17 no. 1 (Graph Theory) ◽  
Author(s):  
Adel Alahmadi ◽  
Robert E. L. Aldred ◽  
Ahmad Alkenani ◽  
Rola Hijazi ◽  
P. Solé ◽  
...  
Keyword(s):  
Graph Theory ◽  
Regular Graph ◽  
Complete Graph ◽  
Hamiltonian Cycle ◽  
Perfect Matching ◽  
Regular Graphs ◽  
Spanning Subgraph ◽  
International Audience ◽  
Matching Extendability

Graph Theory International audience Ruskey and Savage conjectured that in the d-dimensional hypercube, every matching M can be extended to a Hamiltonian cycle. Fink verified this for every perfect matching M, remarkably even if M contains external edges. We prove that this property also holds for sparse spanning regular subgraphs of the cubes: for every d ≥7 and every k, where 7 ≤k ≤d, the d-dimensional hypercube contains a k-regular spanning subgraph such that every perfect matching (possibly with external edges) can be extended to a Hamiltonian cycle. We do not know if this result can be extended to k=4,5,6. It cannot be extended to k=3. Indeed, there are only three 3-regular graphs such that every perfect matching (possibly with external edges) can be extended to a Hamiltonian cycle, namely the complete graph on 4 vertices, the complete bipartite 3-regular graph on 6 vertices and the 3-cube on 8 vertices. Also, we do not know if there are graphs of girth at least 5 with this matching-extendability property.

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