The Minimum Number of Edges in a 3-Connected Graph Where Every Neighborhood Contains a Cycle
This research paper disproves a conjecture about the minimum size of 3-connected locally nonforesty graphs and determines the exact minimum size.
Blow-ups and Extensions of Oriented Trees in Tournaments: Proving Linear Unavoidability
This research paper demonstrates that the families of k-blow-ups and k-extensions of oriented trees are linearly unavoidable, meaning they can always be found within a tournament of a certain size relative to the tree's order.
공-젬 프리 그래프에서의 정점-크리티컬 그래프
본 논문에서는 특정 유형의 그래프(공-젬 프리 그래프)에서 특정 속성(k-정점-크리티컬)을 가진 그래프의 수가 유한함을 증명하고, 이를 통해 이러한 그래프의 색칠 가능성을 판별하는 효율적인 알고리즘 개발에 기여합니다.
On the Finiteness of k-Vertex-Critical Graphs in Co-Gem-Free Graphs with Specific Induced Subgraphs Forbidden
This research paper proves that there are only a finite number of k-vertex-critical graphs within the family of co-gem-free graphs when forbidding certain small graphs (specifically, any graph of order four) as induced subgraphs.
Lines on Quasi-Metric Spaces Defined by Digraphs of Low Diameter
This research paper investigates the validity of a conjecture stating that quasi-metric spaces defined by large enough bridgeless digraphs have at least as many lines as vertices, focusing on digraphs of diameter two and three.
Hoffman Colorings of Graphs: An Exploration of Tightness and Graph Structure
This research paper investigates the conditions under which Hoffman's bound on the chromatic number of a graph is tight, focusing particularly on the structural properties of irregular graphs that meet this bound, known as Hoffman colorable graphs.
Hindrance from a Wasteful Partial Linkage in Infinite Digraphs
In infinite digraphs, a "wasteful partial linkage" - a set of disjoint paths connecting two subsets of vertices where more vertices are left unused in one subset than the other - guarantees the existence of a "hindrance," a structure that obstructs the linking of all vertices in one subset to the other.
Treewidth and Hadwiger Number Relationship in Hereditary Graph Classes
A hereditary graph class exhibits a bounded relationship between treewidth and Hadwiger number if and only if it excludes a planar graph as an induced minor. This relationship can be bounded by a polynomial function, and it is conjectured to be linear.
The Relationship Between Induced Matching Treewidth and Tree-Independence Number in Graphs
Graphs with bounded induced matching treewidth that exclude a fixed biclique as an induced subgraph have bounded tree-independence number, confirming conjectures by Lima et al. and contributing to the understanding of these graph parameters.
트리폭과 클릭 수: 유도 부분 그래프
그래프의 집합이 (tw, ω)-bounded 인지 여부는 해당 그래프 집합의 유도 부분 그래프가 (tw, ω)-bounded 인지 여부와 동일합니다. 즉, 그래프 집합의 트리폭과 클릭 수 사이의 관계는 유도 부분 그래프에도 유지됩니다.
© 2024 by Linnk AI