Cubic TSP - a 1.3-approximation
We prove that every simple bridgeless cubic graph with n >= 8 vertices has a travelling salesman tour of length at most 1.3n - 2, which can be constructed in polynomial time.
cs.DM↗
arXiv subjects
Barbora Candráková
Publications and source records attributed to Barbora Candráková.
Short cycle covers on cubic graphs using chosen 2-factor
We show that every bridgeless cubic graph $G$ with $m$ edges has a cycle cover of length at most $1.6 m$. Moreover, if $G$ does not contain any intersecting circuits of length $5$, then $G$ has a cycle cover of length $212/135 \cdot m \approx 1.570 m$ and if $G$ contains no $5$-circuits, then it has a cycle cover of length at most $14/9 \cdot m \approx 1.556 m$. To prove our results, we show that each $2$-edge-connected cubic graph $G$ on $n$ vertices has a $2$-factor containing at most $n/10+f(G)$ circuits of length $5$, where the value of $f(G)$ only depends on the presence of several subgraphs arising from the Petersen graph. As a corollary we get that each $3$-edge-connected cubic graph on $n$ vertices has a $2$-factor containing at most $n/9$ circuits of length $5$ and each $4$-edge-connected cubic graph on $n$ vertices has a $2$-factor containing at most $n/10$ circuits of length $5$.
math.CO↗
Avoiding 5-circuits in a 2-factor of cubic graphs
We show that every bridgeless cubic graph $G$ on $n$ vertices other than the Petersen graph has a 2-factor with at most $2(n-2)/15$ circuits of length $5$. An infinite family of graphs attains this bound. We also show that $G$ has a 2-factor with at most $n/5.8\overline{3}$ odd circuits. This improves the previously known bound of $n/5.41$ [Lukoťka, Máčajová, Mazák, Škoviera: Small snarks with large oddness, arXiv:1212.3641 [cs.DM] ].
math.CO↗