TY - JOUR
T1 - The Matching Extendability of Optimal 1-Planar Graphs
AU - Fujisawa, Jun
AU - Segawa, Keita
AU - Suzuki, Yusuke
N1 - Funding Information:
Y. Suzuki: Partly supported by Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C) 16K05250.
Funding Information:
J. Fujisawa: Partly supported by Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (B) 16H03952 and (C) 17K05349 and Grant-in-Aid for Young Scientists (B) 26800085.
Publisher Copyright:
© 2018, Springer Japan KK, part of Springer Nature.
PY - 2018/9/1
Y1 - 2018/9/1
N2 - A graph G is said to be 1-planar if it can be drawn on the sphere or plane so that any edge of G has at most one crossing point with another edge. Moreover, G is called an optimal 1-planar graph if | E(G) | = 4 | V(G) | - 8. In this paper, we investigate the matching extendability of optimal 1-planar graphs. It is shown that every optimal 1-planar graph G of even order is 2-extendable unless G contains a 4-cycle C which separates the graph into two odd components. Moreover, for any 5-connected optimal 1-planar graph, we characterize a matching with three edges which is not extendable.
AB - A graph G is said to be 1-planar if it can be drawn on the sphere or plane so that any edge of G has at most one crossing point with another edge. Moreover, G is called an optimal 1-planar graph if | E(G) | = 4 | V(G) | - 8. In this paper, we investigate the matching extendability of optimal 1-planar graphs. It is shown that every optimal 1-planar graph G of even order is 2-extendable unless G contains a 4-cycle C which separates the graph into two odd components. Moreover, for any 5-connected optimal 1-planar graph, we characterize a matching with three edges which is not extendable.
KW - Extendability
KW - Optimal 1-planar graph
KW - Perfect matching
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U2 - 10.1007/s00373-018-1932-6
DO - 10.1007/s00373-018-1932-6
M3 - Article
AN - SCOPUS:85051283740
SN - 0911-0119
VL - 34
SP - 1089
EP - 1099
JO - Graphs and Combinatorics
JF - Graphs and Combinatorics
IS - 5
ER -