Results 191 to 200 of about 1,402,601 (292)

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

open access: yesJournal 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   +3 more
wiley   +1 more source

Weak Degeneracy of Planar Graphs

open access: yesJournal 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   +2 more
wiley   +1 more source

Linear Versus Centred Colouring via Pseudogrids

open access: yesJournal of Graph Theory, EarlyView.
ABSTRACT A centred colouring of a graph is a vertex colouring in which every connected subgraph contains a vertex whose colour is unique and a linear colouring is a vertex colouring in which every (not‐necessarily induced) path contains a vertex whose colour is unique. For a graph G $G$, the centred chromatic number χ cen ( G ) ${\chi }_{\text{cen}}(G)$
Prosenjit Bose   +4 more
wiley   +1 more source

On Fork‐Free t‐Perfect Graphs

open access: yesJournal of Graph Theory, EarlyView.
ABSTRACT In an effort to understand the complexity of the maximum independent set problem, Chvátal introduced t‐perfect graphs. While a full characterization of this class remains open, important progress has been made for claw‐free graphs [Bruhn and Stein, Math. Program. 2012] and P 5 ${P}_{5}$‐free graphs [Bruhn and Fuchs, SIAM J. Discrete Math. 2017]
Yixin Cao, Shenghua Wang
wiley   +1 more source

Chromatic Ramsey Numbers and Two‐Color Turán Densities

open access: yesJournal of Graph Theory, EarlyView.
ABSTRACT Given a graph G, its 2‐color Turán number ex ( 2 ) ( n , G ) is the maximum number of edges in an n‐vertex graph, such that the edges can be colored with two colors avoiding a monochromatic copy of G. Let π ( 2 ) ( G ) = lim n → ∞ ex ( 2 ) ( n , G ) / n 2 be the 2‐color Turán density of G.
Maria Axenovich, Simon Gaa, Dingyuan Liu
wiley   +1 more source

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