Smallest cubic graphs with given girth and skewness

CL Ng, GL Chia, DCK Wong - ITM Web of Conferences, 2024 - itm-conferences.org
The skewness of a graph is the minimum number of its edges whose deletion results in a
planar graph. We determine the minimum orders of cubic graphs with girth no more than 6 …

On the skewness of products of graphs

GL Chia, KA Sim - Discrete Applied Mathematics, 2024 - Elsevier
The skewness of a graph G is the minimum number of edges in G whose deletion results in
a planar graph. We determine the skewness (i) of the Cartesian product of G with path and …

On the skewness of the generalized Heawood graphs

CL Ng, GL Chia, DCK Wong - AKCE International Journal of …, 2024 - Taylor & Francis
By the skewness of a graph, we mean the minimum number of its edges whose deletion
results in a planar graph. We determine the skewness of a large family of cubic bipartite …

Properties of π-skew Graphs with Applications

ZD Ouyang, FM Dong, RX Zhang, EG Tay - Acta Mathematica Sinica …, 2021 - Springer
The skewness of a graph G, denoted by sk (G), is the minimum number of edges in G whose
removal results in a planar graph. It is an important parameter that measures how close a …

[PDF][PDF] Maximal k-degenerate spanning subgraphs

N Krisam, L Merker - 2021 - i11www.iti.kit.edu
In this thesis we discuss maximum k-degenerate spanning subgraphs. A spanning subgraph
is a subgraph where only edges were deleted. In a k-degenerate graph G every subgraph of …

[HTML][HTML] On the skewness of Cartesian products with trees

Z Ouyang, F Dong, EG Tay - Discrete Applied Mathematics, 2019 - Elsevier
The skewness of a graph G is the minimum number of edges in G whose removal results in
a planar graph. It is a parameter that measures how non-planar a graph is, and it also has …

[PDF][PDF] Skewness and the crossing numbers of graphs

Z Ding - AIMS Mathematics, 2023 - aimspress.com
The skewness of a graph G, sk (G), is the smallest number of edges that need to be removed
from G to make it planar. The crossing number of a graph G, cr (G), is the minimum number …

A proof technique for skewness of graphs

GL Chia, CL Lee, YH Ling - arXiv preprint arXiv:1709.06280, 2017 - arxiv.org
The skewness of a graph G is the minimum number of edges in G whose removal results in
a planar graph. By appropriately introducing a weight to each edge of a graph, we …

Triangulability of Convex Graphs and Convex Skewness

NA Ali, GL Chia, HM Trao, A Kilicman - arXiv preprint arXiv:1611.09033, 2016 - arxiv.org
Motivated by a result of [1] which states that if F is a subgraph of a convex complete graph
K_n and F contains no boundary edge of K_n and| E (F)|\leq n-3, then K_n-F admits a …

Triangulability of convex graphs and convex skewness

NA Ali, GL Chia, HM Trao, A Kilicman - … Algorithms and Applications, 2022 - World Scientific
Suppose F is a subgraph of a convex complete graph K n and F contains no boundary edge
of K n and| E (F)|≤ n− 1. We determine necessary and sufficient conditions on F such that K …