TY - JOUR
T1 - Perfect matchings avoiding prescribed edges in a star-free graph
AU - Egawa, Yoshimi
AU - Fujisawa, Jun
AU - Plummer, Michael D.
AU - Saito, Akira
AU - Yamashita, Tomoki
N1 - Funding Information:
J. Fujisawa’s research was supported by Japan Society for the Promotion of Science , Grant-in-Aid for Young Scientists (B), 22740068 , 2012 and 2013, and 26800085 , 2014, and Keio Gijuku Academic Development Funds. A. Saito’s research was supported by Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), 22500018 , 2012 and 25330017 , 2013 and 2014.
Publisher Copyright:
© 2015 Elsevier B.V. All rights reserved.
PY - 2015/6/22
Y1 - 2015/6/22
N2 - Aldred and Plummer (1999) have proved that every m-connected K1,m-k+2-free graph of even order contains a perfect matching which avoids k prescribed edges. They have also proved that the result is best possible in the range 1≤k≤12(m+1). In this paper, we show that if 12(m+2)≤k≤m-1, their result is not best possible. We prove that if m≥4 and 12(m+2)≤k≤m-1, every K1,⌈2m-k+43⌉-free graph of even order contains a perfect matching which avoids k prescribed edges. While this is a best possible result in terms of the order of a forbidden star, if 2m-k+4≡0(mod3), we also prove that only finitely many sharpness examples exist.
AB - Aldred and Plummer (1999) have proved that every m-connected K1,m-k+2-free graph of even order contains a perfect matching which avoids k prescribed edges. They have also proved that the result is best possible in the range 1≤k≤12(m+1). In this paper, we show that if 12(m+2)≤k≤m-1, their result is not best possible. We prove that if m≥4 and 12(m+2)≤k≤m-1, every K1,⌈2m-k+43⌉-free graph of even order contains a perfect matching which avoids k prescribed edges. While this is a best possible result in terms of the order of a forbidden star, if 2m-k+4≡0(mod3), we also prove that only finitely many sharpness examples exist.
KW - Extendability
KW - Forbidden subgraph
KW - Perfect matching
KW - Star-free graphs
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U2 - 10.1016/j.disc.2015.05.014
DO - 10.1016/j.disc.2015.05.014
M3 - Article
AN - SCOPUS:84934982199
SN - 0012-365X
VL - 338
SP - 2260
EP - 2274
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 12
ER -