Results 81 to 90 of about 2,876,957 (249)

Saturated Partial Embeddings of Planar Graphs

Journal of Graph Theory, EarlyView.
ABSTRACT In this work, we study how far one can deviate from optimal behavior when embedding a planar graph. For a planar graph G $G$, we say that a plane subgraph H ⊆ G $H\subseteq G$ is a plane‐saturated subgraph if adding any edge (possibly with new vertices) to H $H$ would either violate planarity or make the resulting graph no longer a subgraph of
Alexander Clifton, Nika Salia
wiley   +1 more source

Regular embeddings of complete bipartite maps: classification and enumeration

The regular embeddings of complete bipartite graphs Kn, n in orientable surfaces are classified and enumerated, and their automorphism groups and combinatorial properties are determined.
Jones, Gareth
core   +1 more source

A Note on Lovász Characterization of Perfect Graphs

Journal of Graph Theory, EarlyView.
ABSTRACT A graph is perfect if, for every induced subgraph, the chromatic number equals the size of its largest clique. In 1972, Lovász established a fundamental characterization of perfect graphs, showing that a graph is perfect if and only if, for every induced subgraph, the product of the size of the largest independent set and the size of the ...
James Alex
wiley   +1 more source

Characterization of Graphs Without Even F $F$‐Orientations

Journal of Graph Theory, EarlyView.
ABSTRACT A graph G $G$ is 1‐extendable if every edge belongs to at least one 1‐factor of G $G$. Let G $G$ be a graph with a 1‐factor F $F$. Then an even (odd) F $F$ ‐orientation of G $G$ is an orientation in which each F $F$‐alternating cycle has exactly an even (odd) number of edges directed in the same fixed direction around the cycle.
Marién Abreu, Domenico Labbate, Federico Romaniello, John Sheehan   +3 more
wiley   +1 more source

On Graphs Which Have Locally Complete 2‐Edge‐colourings and Their Relationship to Proper Circular‐Arc Graphs

Journal of Graph Theory, EarlyView.
ABSTRACT A 2‐edge‐coloured graph G $G$ is called locally complete if for each vertex v $v$, the vertices adjacent to v $v$ through edges of the same colour induce a complete subgraph in G $G$. Locally complete 2‐edge‐coloured graphs have nice properties, and there exists a polynomial algorithm to decide whether such a graph has an alternating ...
Jørgen Bang‐Jensen, Jing Huang
wiley   +1 more source

The study of the star arboricity of complete bipartite graphs

, 2010
碩士假設V1﹐V2為兩個集合﹐若V＝V1∪V2﹐V1∩V2＝Φ且E＝{uv︱u V1, v V2}﹐則稱(V, E)為完全二分圖。若︱V1︱＝m﹐︱V2︱＝n﹐則此完全二分圖記為Km,n。當︱V1︱＝1﹐︱V2︱＝n﹐稱K1,n為星圖﹙Star﹚。當圖G的每一個最大連通子圖都是星圖時﹐我們稱圖G為星林圖﹙Star-forest﹚。將圖G分割成邊相異之星林圖時﹐其最少星林圖的個數稱為G的星林分解數﹐用*(G)表示。 在本論文中﹐我們考慮的是完全二分圖K2n,2n+4﹐n≧3的星林分解數 ...
廖藝淳; Liao, Yi-chun
core   +1 more source

Quantum Counting on the Complete Bipartite Graph [PDF]

, 2023
Quantum counting is a key quantum algorithm that aims to determine the number of marked elements in a database. This algorithm is based on the quantum phase estimation algorithm and uses the evolution operator of Grover's algorithm because its non ...
Bezerra, Gustavo A., Santos, Raqueline A. M., Portugal, Renato   +2 more
core   +1 more source

The 1 3 $\frac{1}{3}$‐Conjectures for Domination in Cubic Graphs

Journal of Graph Theory, EarlyView.
ABSTRACT A set S $S$ of vertices in a graph G $G$ is a dominating set of G $G$ if every vertex not in S $S$ is adjacent to a vertex in S $S$. The domination number of G $G$, denoted by γ ( G ) $\gamma (G)$, is the minimum cardinality among all dominating sets in G $G$. In a breakthrough paper in 2008, Löwenstein and Rautenbach proved that if G $G$ is a
Paul Dorbec, Michael A. Henning
wiley   +1 more source

Minimal free resolutions of complete bipartite graph ideals [PDF]

, 2020
. This paper gives an explicit construction for the minimal free resolution of a complete bipartite graph ideal. This yields a combinatorial formula for the Betti numbers and projective dimension of complete bipartite graph ideals. The question of how to
Daniel Visscher
core  

Cluttered orderings for the complete bipartite graph [PDF]

, 2005
To minimize the access cost in large disk arrays (RAID) Cohen, Colbourn, and Froncek introduced and investigated in a series of papers the concept of (d,f)-cluttered orderings of various set systems, d,f∈N.
Jimbo, Masakazu, Müller, Meinard, Adachi, Tomoko   +2 more
core   +1 more source