Results 81 to 90 of about 756 (218)

Chordal Completions of Planar Graphs

Journal of Combinatorial Theory, Series B, 1994
A graph is chordal if there are no induced cycles of length 4 or more. A chordal completion of a graph is formed by adding edges until the resulting graph is chordal. What is the minimal number of edges in a chordal completion? The authors answer this question for the class of planar graphs: every planar graph on \(n\) vertices has a chordal completion
Fan R. K. Chung, David Mumford
openaire   +2 more sources

Majorbio Cloud: An integrated platform for single‐omics and integrated multi‐omics analysis of microbiome and metabolome

iMetaOmics, EarlyView.
Advances in sequencing and mass spectrometry have propelled life sciences into the multi‐omics era. Metabolomics and microbiomics are widely applied across various research fields, yet massive data analysis faces challenges like limited tool functionality and high technical barriers.
Jianhua Zhao, Linmeng Liu, Bing Yang, Mengxi Li, Junbiao Zhang, Jichen Han, Xiaodan Li, Yan Wang, Shaobing Du, Qianhui Han, Linna Zhang, Wenjuan Sun, Hao Gao, Yachen Dong, Huasheng Huang, Xianglin Zhang, Kegang Yu   +16 more
wiley   +1 more source

Lower Bounds for Maximum Weight Bisections of Weighted Triangle‐Free Subcubic Graphs

Journal of Graph Theory, EarlyView.
ABSTRACT A bisection of a graph is a cut in which the number of vertices in the two parts of the cut differ by at most 1. In this paper, we consider maximum weight bisections of edge‐weighted triangle‐free subcubic graphs and show that every weighted triangle‐free subcubic graph G = ( V , E , w ) $G=(V,E,w)$ has a bisection with weight at least θ ⋅ w (
Stefanie Gerke, Gregory Gutin, Anders Yeo, Yacong Zhou   +3 more
wiley   +1 more source

Stable Cuts, NAC‐Colourings and Flexible Realisations of Graphs

Journal of Graph Theory, EarlyView.
ABSTRACT A (2‐dimensional) realisation of a graph G $G$ is a pair ( G , p ) $(G,p)$, where p $p$ maps the vertices of G $G$ to R 2 ${{\mathbb{R}}}^{2}$. A realisation is flexible if it can be continuously deformed while keeping the edge lengths fixed, and rigid otherwise.
Katie Clinch, Dániel Garamvölgyi, John Haslegrave, Tony Huynh, Jan Legerský, Anthony Nixon   +5 more
wiley   +1 more source

Strongly chordal and chordal bipartite graphs are sandwich monotone

Journal of Combinatorial Optimization, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pinar Heggernes, Federico Mancini 0001, Charis Papadopoulos, R. Sritharan   +3 more
openaire   +3 more sources

Weak Degeneracy of Planar Graphs

Journal of Graph Theory, EarlyView.
ABSTRACT The weak degeneracy of a graph G $G$ is a numerical parameter that was recently introduced by the first two authors with the aim of understanding the power of greedy algorithms for graph coloring. Every d $d$‐degenerate graph is weakly d $d$‐degenerate, but the converse is not true in general (e.g., all connected d $d$‐regular graphs except ...
Anton Bernshteyn, Eugene Lee, Evelyne Smith‐Roberge   +2 more
wiley   +1 more source

On the 2-token graph of a graph

AKCE International Journal of Graphs and Combinatorics, 2020
Let be a graph and let be a positive integer. Let = and . The -token graph is the graph with vertex set and two vertices and are adjacent if and , where denotes the symmetric difference. In this paper we present several basic results on 2-token graphs.
J. Deepalakshmi, G. Marimuthu, A. Somasundaram, S. Arumugam   +3 more
doaj   +1 more source

A Min–Max Relation on Dicuts and Dijoins in Weighted Chordal Digraphs

Journal of Graph Theory, EarlyView.
ABSTRACT In a digraph, a dicut is a cut where all the arcs cross in one direction. A dijoin is a subset of arcs that intersects every dicut. Edmonds and Giles conjectured that in a weighted digraph, the minimum weight of a dicut is equal to the maximum size of a packing of dijoins. This has been disproved. However, the unweighted version conjectured by
Gérard Cornuéjols, Siyue Liu, R. Ravi
wiley   +1 more source

Explicit 3‐colorings for Exponential Graphs

Journal of Graph Theory, EarlyView.
ABSTRACT In 1985, El‐Zahar and Sauer showed that the chromatic number of the direct product of two 4‐chromatic graphs is 4, establishing a nontrivial case of Hedetniemi's conjecture, which has since been refuted in general. Their proof uses the concept of an exponential graph, showing that if a graph H $H$ has no proper 3‐coloring, then the exponential
Adrien Argento, Pierre Charbit, Alantha Newman   +2 more
wiley   +1 more source

Cohen–Macaulay chordal graphs

Journal of Combinatorial Theory, Series A, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jürgen Herzog, Takayuki Hibi, Xinxian Zheng   +2 more
openaire   +1 more source