Nonempty intersection of longest paths in a graph with a small matching number

Fuyuan Chen

Czechoslovak Mathematical Journal (2015)

  • Volume: 65, Issue: 2, page 545-553
  • ISSN: 0011-4642

Abstract

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A maximum matching of a graph G is a matching of G with the largest number of edges. The matching number of a graph G , denoted by α ' ( G ) , is the number of edges in a maximum matching of G . In 1966, Gallai conjectured that all the longest paths of a connected graph have a common vertex. Although this conjecture has been disproved, finding some nice classes of graphs that support this conjecture is still very meaningful and interesting. In this short note, we prove that Gallai’s conjecture is true for every connected graph G with α ' ( G ) ≤ 3 .

How to cite

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Chen, Fuyuan. "Nonempty intersection of longest paths in a graph with a small matching number." Czechoslovak Mathematical Journal 65.2 (2015): 545-553. <http://eudml.org/doc/270121>.

@article{Chen2015,
abstract = {A maximum matching of a graph $G$ is a matching of $G$ with the largest number of edges. The matching number of a graph $G$, denoted by $\alpha ^\{\prime \}(G)$, is the number of edges in a maximum matching of $G$. In 1966, Gallai conjectured that all the longest paths of a connected graph have a common vertex. Although this conjecture has been disproved, finding some nice classes of graphs that support this conjecture is still very meaningful and interesting. In this short note, we prove that Gallai’s conjecture is true for every connected graph $G$ with $\alpha ^\{\prime \}(G)\le 3$.},
author = {Chen, Fuyuan},
journal = {Czechoslovak Mathematical Journal},
keywords = {longest path; matching number},
language = {eng},
number = {2},
pages = {545-553},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Nonempty intersection of longest paths in a graph with a small matching number},
url = {http://eudml.org/doc/270121},
volume = {65},
year = {2015},
}

TY - JOUR
AU - Chen, Fuyuan
TI - Nonempty intersection of longest paths in a graph with a small matching number
JO - Czechoslovak Mathematical Journal
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 2
SP - 545
EP - 553
AB - A maximum matching of a graph $G$ is a matching of $G$ with the largest number of edges. The matching number of a graph $G$, denoted by $\alpha ^{\prime }(G)$, is the number of edges in a maximum matching of $G$. In 1966, Gallai conjectured that all the longest paths of a connected graph have a common vertex. Although this conjecture has been disproved, finding some nice classes of graphs that support this conjecture is still very meaningful and interesting. In this short note, we prove that Gallai’s conjecture is true for every connected graph $G$ with $\alpha ^{\prime }(G)\le 3$.
LA - eng
KW - longest path; matching number
UR - http://eudml.org/doc/270121
ER -

References

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