A sufficient condition for a balanced bipartite digraph to be hamiltonian
Discrete mathematics & theoretical computer science, Tome 19 (2017-2018) no. 3
We describe a new type of sufficient condition for a balanced bipartite digraph to be hamiltonian. Let $D$ be a balanced bipartite digraph and $x,y$ be distinct vertices in $D$. $\{x, y\}$ dominates a vertex $z$ if $x\rightarrow z$ and $y\rightarrow z$; in this case, we call the pair $\{x, y\}$ dominating. In this paper, we prove that a strong balanced bipartite digraph $D$ on $2a$ vertices contains a hamiltonian cycle if, for every dominating pair of vertices $\{x, y\}$, either $d(x)\ge 2a-1$ and $d(y)\ge a+1$ or $d(x)\ge a+1$ and $d(y)\ge 2a-1$. The lower bound in the result is sharp.
@article{DMTCS_2017_19_3_a10,
author = {Wang, Ruixia},
title = {A sufficient condition for a balanced bipartite digraph to be hamiltonian},
journal = {Discrete mathematics & theoretical computer science},
year = {2017-2018},
volume = {19},
number = {3},
doi = {10.23638/DMTCS-19-3-11},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-19-3-11/}
}
TY - JOUR AU - Wang, Ruixia TI - A sufficient condition for a balanced bipartite digraph to be hamiltonian JO - Discrete mathematics & theoretical computer science PY - 2017-2018 VL - 19 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-19-3-11/ DO - 10.23638/DMTCS-19-3-11 LA - en ID - DMTCS_2017_19_3_a10 ER -
%0 Journal Article %A Wang, Ruixia %T A sufficient condition for a balanced bipartite digraph to be hamiltonian %J Discrete mathematics & theoretical computer science %D 2017-2018 %V 19 %N 3 %U http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-19-3-11/ %R 10.23638/DMTCS-19-3-11 %G en %F DMTCS_2017_19_3_a10
Wang, Ruixia. A sufficient condition for a balanced bipartite digraph to be hamiltonian. Discrete mathematics & theoretical computer science, Tome 19 (2017-2018) no. 3. doi: 10.23638/DMTCS-19-3-11
Cité par Sources :