Spreading in Claw-Free Cubic Graphs: Determining (p, q)-Spreading Numbers
This research paper investigates (p, q)-spreading in claw-free cubic graphs, determining the exact (p, q)-spreading number for most cases or narrowing it down to two possible values, thereby advancing the understanding of dynamic coloring processes in this specific graph class.
Finding Minimum Tournament Sizes for Immersions of Transitive Tournaments and Complete Digraphs
This research paper investigates the minimum size of a tournament required to guarantee the existence of immersions of transitive tournaments and complete digraphs, providing tight bounds and efficient algorithms for finding these immersions.
The Dib-Chromatic Number of Digraphs: Exploring Acyclic Vertex Colorings
This research paper introduces the concept of the dib-chromatic number, a novel parameter for analyzing digraphs based on acyclic vertex colorings, and explores its properties, bounds, and applications in various digraph classes.
Embedding Oriented Trees in Digraphs: Degree Conditions and the Exclusion of Oriented 4-Cycles
This research paper investigates sufficient conditions for embedding oriented trees into digraphs, focusing on minimum degree conditions and the exclusion of oriented 4-cycles as key factors influencing successful embeddings.
연결 그래프의 교차 패밀리를 위한 강한 방향성
연결 그래프에서 각 교차 집합에 대해 최소 하나의 나가는 간선과 하나의 들어오는 간선을 갖도록 하는 강한 방향성이 항상 존재한다는 것을 증명하여, 가중치가 적용된 다이그래프에서의 에지 분할 문제인 Edmonds-Giles 추측에 대한 반례에서 가중치 1의 간선들은 연결될 수 없다는 것을 보여줍니다.
Strong Orientation of Connected Graphs for Crossing Families: A Resolution to a Conjecture in Dijoin Packing
Any connected graph with a crossing family of vertex subsets, where each subset has at least two edges connecting it to the rest of the graph, can be strongly oriented for that family. This implies that in a minimal counterexample to the Edmonds-Giles conjecture with minimum dicut weight 2, the arcs of nonzero weight must be disconnected.
On the Conditions for Corona Graphs to be k-König-Egerváry Graphs (for k=0,1)
This research paper provides necessary and sufficient conditions for the corona of graphs to be a König-Egerváry graph or a 1-König-Egerváry graph, focusing on the relationship between the graph's structure and its independence and matching numbers.
Embedding Clique Immersions and Subdivisions in Sparse Expanders: An Asymptotic Analysis
This research paper investigates the existence of large topological cliques (immersions and subdivisions) within sparse expander graphs, demonstrating their presence under specific conditions and advancing our understanding of extremal graph theory.
Finding Regular Subgraphs in Graphs: Determining the Minimum Average Degree Requirement
This paper resolves the Erdős–Sauer problem, determining that the minimum average degree required for an n-vertex graph to guarantee an r-regular subgraph exhibits a phase transition: Θ(r² log log n) for r < (log n)¹⁻ᵟ and Θ(r log(n/r)) for r ≥ log n.
The Perfect Matching Hamiltonian Property in Prism and Crossed Prism Graphs: An Investigation
This research paper investigates the Perfect Matching Hamiltonian (PMH) property in two specific families of cubic graphs: Prism graphs (Pn) and Crossed Prism graphs (CPn), concluding that only the Cube graph (P4) among Prism graphs and CPn graphs with even n exhibit the PMH property.
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