Geodesic
Even cycles and perfect matchings in claw-free plane graphs
Discrete mathematics & theoretical computer science, Tome 22 (2020-2021) no. 4.

Voir la notice de l'article provenant de la source Episciences

Lov{\'a}sz showed that a matching covered graph $G$ has an ear decomposition starting with an arbitrary edge of $G$. Let $G$ be a graph which has a perfect matching. We call $G$ cycle-nice if for each even cycle $C$ of $G$, $G-V(C)$ has a perfect matching. If $G$ is a cycle-nice matching covered graph, then $G$ has ear decompositions starting with an arbitrary even cycle of $G$. In this paper, we characterize cycle-nice claw-free plane graphs. We show that the only cycle-nice simple 3-connected claw-free plane graphs are $K_4$, $W_5$ and $\overline C_6$. Furthermore, every cycle-nice 2-connected claw-free plane graph can be obtained from a graph in the family ${\cal F}$ by a sequence of three types of operations, where ${\cal F}$ consists of even cycles, a diamond, $K_4$, and $\overline C_6$.
DOI : 10.23638/DMTCS-22-4-6
Classification : 05C10, 05C38 
@article{DMTCS_2020_22_4_a7,
     author = {Zhang, Shanshan and Wang, Xiumei and Yuan, Jinjiang},
     title = {Even cycles and perfect matchings in claw-free plane graphs},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {22},
     number = {4},
     year = {2020-2021},
     doi = {10.23638/DMTCS-22-4-6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-22-4-6/}
}
TY  - JOUR
AU  - Zhang, Shanshan
AU  - Wang, Xiumei
AU  - Yuan, Jinjiang
TI  - Even cycles and perfect matchings in claw-free plane graphs
JO  - Discrete mathematics & theoretical computer science
PY  - 2020-2021
VL  - 22
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-22-4-6/
DO  - 10.23638/DMTCS-22-4-6
LA  - en
ID  - DMTCS_2020_22_4_a7
ER  - 
%0 Journal Article
%A Zhang, Shanshan
%A Wang, Xiumei
%A Yuan, Jinjiang
%T Even cycles and perfect matchings in claw-free plane graphs
%J Discrete mathematics & theoretical computer science
%D 2020-2021
%V 22
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-22-4-6/
%R 10.23638/DMTCS-22-4-6
%G en
%F DMTCS_2020_22_4_a7
Zhang, Shanshan; Wang, Xiumei; Yuan, Jinjiang. Even cycles and perfect matchings in claw-free plane graphs. Discrete mathematics & theoretical computer science, Tome 22 (2020-2021) no. 4. doi : 10.23638/DMTCS-22-4-6. http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-22-4-6/

Cité par Sources :