arXiv subjects

Chenglong Deng

Publications and source records attributed to Chenglong Deng.

3 recordsLinked to original sources

arXiv2026

Optimal binding function for (cap,even hole)-free graphs with no short odd holes

A hole in a graph is an induced cycle of length at least $4$. A cap is a hole together with a vertex adjacent to exactly two consecutive vertices of it. Chen, Xu and Xu conjectured that if $q\ge2$ and $G$ is a $(\mathrm{cap},\mathrm{even\ hole})$-free graph with no odd hole of length at most $2q-1$, then $\chi(G)\le \left\lceil \frac{2q+1}{2q}\omega(G)\right\rceil.$ They confirmed the conjecture for $q \le 3$. In this paper, we prove the conjecture for all $q \ge 3$. As a corollary, we prove that for such a graph $G$, $\chi_f(G)\le \frac{2q+1}{2q}\omega(G).$

math.CO↗

arXiv2024

Truncated degree AT-orientations of outerplanar graphs

An AT-orientation of a graph $G$ is an orientation $D$ of $G$ such that the number of even Eulerian sub-digraphs and the number of odd Eulerian sub-digraphs of $D$ are distinct. Given a mapping $f: V(G) \to \mathbb{N}$, we say $G$ is $f$-AT if $G$ has an AT-orientation $D$ with $ < f(v)$ for each vertex $v$. For a positive integer $k$, we say $G$ is $k$-truncated degree-AT if $G$ is $f$-AT for the mapping $f$ defined as $f(v) = \min #{k, d_G(v)#} $. This paper proves that 2-connected outerplanar graphs other than odd cycles are $5$-truncated degree-AT, and 2-connected bipartite outerplanar graphs are $4$-truncated degree-AT. As a consequence, 2-connected outerplanar graphs other than odd cycles are $5$-truncated degree paintable, and 2-connected bipartite outerplanar graphs are $4$-truncated degree paintable. This improves the result of Hutchinson in [On list-coloring outerplanar graphs], where it was proved that maximal 2-connected outerplanar graphs other than are 5-truncated degree-choosable, and 2-connected bipartite outerplanar graphs are 4-truncated degree-choosable.

math.CO↗

arXiv2024

Persistent but weak magnetic field at Moon's midlife revealed by Chang'e-5 basalt

The evolution of the lunar magnetic field can reveal the Moon's interior structure, thermal history, and surface environment. The mid-to-late stage evolution of the lunar magnetic field is poorly constrained, and thus the existence of a long-lived lunar dynamo remains controversial. The Chang'e-5 mission returned the heretofore youngest mare basalts from Oceanus Procellarum uniquely positioned at mid-latitude. We recovered weak paleointensities of 2-4 uT from the Chang'e-5 basalt clasts at 2 billion years ago, attestting to the longevity of a lunar dynamo until at least the Moon's midlife. This paleomagnetic result implies the existence of thermal convection in the lunar deep interior at the lunar mid-stage which may have supplied mantle heat flux for the young volcanism.

physics.geo-ph↗