The Maximum Clique Problem and Integer Programming Models, Their Modifications, Complexity and Implementation
M Seda - Symmetry, 2023 - mdpi.com
The maximum clique problem is a problem that takes many forms in optimization and related
graph theory problems, and also has many applications. Because of its NP-completeness …
graph theory problems, and also has many applications. Because of its NP-completeness …
[HTML][HTML] A conjecture for the Clique number of graphs associated with symmetric numerical semigroups of arbitrary multiplicity and embedding dimension
AS Alali, MA Binyamin, M Mehtab - Symmetry, 2024 - mdpi.com
A subset S of non-negative integers N o is called a numerical semigroup if it is a submonoid
of N o and has a finite complement in N o. An undirected graph G (S) associated with S is a …
of N o and has a finite complement in N o. An undirected graph G (S) associated with S is a …
The reducibility of optimal 1-planar graphs with respect to the lexicographic product
L Zhang, Y Huang - arXiv preprint arXiv:2211.14733, 2022 - arxiv.org
A graph is called 1-planar if it can be drawn on the plane (or on the sphere) such that each
edge is crossed at most once. A 1-planar graph $ G $ is called optimal if it satisfies $| E (G) …
edge is crossed at most once. A 1-planar graph $ G $ is called optimal if it satisfies $| E (G) …
Extremal number of cliques of given orders in graphs with a forbidden clique minor
R Shi, F Wei - arXiv preprint arXiv:2408.12082, 2024 - arxiv.org
Alon and Shikhelman initiated the systematic study of a generalization of the extremal
function. Motivated by algorithmic applications, the study of the extremal function $\text …
function. Motivated by algorithmic applications, the study of the extremal function $\text …
On the Edge-Connectivity and Restricted Edge-Connectivity of Optimal 1-Planar Graphs
L Zhang, Y Huang, G Wang - Bulletin of the Malaysian Mathematical …, 2024 - Springer
A graph is called 1-planar if it can be drawn on the plane (or on the sphere) such that each
edge is crossed at most once. It is known that a 1-planar graph G with at least three vertices …
edge is crossed at most once. It is known that a 1-planar graph G with at least three vertices …
Maximum degree and connectivity on claw-free -planar graphs
L Zhang, Z Ouyang, Y Huang - arXiv preprint arXiv:2501.15124, 2025 - arxiv.org
The study of claw-free planar graphs dates back to Plummer's work in 1989. Plummer
showed that the maximum degree of every 3-connected claw-free planar graph is at most 6 …
showed that the maximum degree of every 3-connected claw-free planar graph is at most 6 …
4-connected 1-planar chordal graphs are Hamiltonian-connected
L Zhang, Y Huang, S Lv, F Dong - arXiv preprint arXiv:2404.15663, 2024 - arxiv.org
Tutte proved that 4-connected planar graphs are Hamiltonian. It is unknown if there is an
analogous result on 1-planar graphs. In this paper, we characterize 4-connected 1-planar …
analogous result on 1-planar graphs. In this paper, we characterize 4-connected 1-planar …