Results 21 to 30 of about 39,180 (264)
Perfect edge domination in vague graphs
Ratio Mathematica, 2021 In this paper, we modified undirected vague graphs and edge domination set based on these two concepts. We study the notions of perfect edge domination, connected perfect edge domination of vague graph. Moreover, we investigate some related properties in
M Kaliraja, P Kanibose, Abdul Ibrahim
doaj +1 more source
Some Variations of Perfect Graphs
Discussiones Mathematicae Graph Theory, 2016 We consider (ψk−γk−1)-perfect graphs, i.e., graphs G for which ψk(H) = γk−1(H) for any induced subgraph H of G, where ψk and γk−1 are the k-path vertex cover number and the distance (k − 1)-domination number, respectively.
Dettlaff Magda +3 more
doaj +1 more source
On the chromatic number of (P_{5},windmill)-free graphs [PDF]
Opuscula Mathematica, 2017 In this paper we study the chromatic number of \((P_5, windmill)\)-free graphs. For integers \(r,p\geq 2\) the windmill graph \(W_{r+1}^p=K_1 \vee pK_r\) is the graph obtained by joining a single vertex (the center) to the vertices of \(p\) disjoint ...
Ingo Schiermeyer
doaj +1 more source
Characterising and recognising game-perfect graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 Consider a vertex colouring game played on a simple graph with $k$ permissible colours. Two players, a maker and a breaker, take turns to colour an uncoloured vertex such that adjacent vertices receive different colours.
Dominique Andres, Edwin Lock
doaj +1 more source
Electronic Notes in Discrete Mathematics, 2013 Abstract In this paper we study a natural generalization for the perfection of graphs to other interesting parameters related with colorations. This generalization was introduced partially by Christen and Selkow in 1979 and Yegnanarayanan in 2001. Let a , b ∈ { ω , χ , Γ , α , ψ } where ω is the clique number, χ is the chromatic ...
Gabriela Araujo-Pardo +1 more
openaire +1 more source
Perfect codes in power graphs of finite groups
Open Mathematics, 2017 The power graph of a finite group is the graph whose vertex set is the group, two distinct elements being adjacent if one is a power of the other. The enhanced power graph of a finite group is the graph whose vertex set consists of all elements of the ...
Ma Xuanlong +4 more
doaj +1 more source
Contractions in perfect graphs
Discrete Applied MathematicsIn this paper, we characterize the class of {\em contraction perfect} graphs which are the graphs that remain perfect after the contraction of any edge set. We prove that a graph is contraction perfect if and only if it is perfect and the contraction of any single edge preserves its perfection.
Alexandre Dupont-Bouillard +3 more
openaire +2 more sources
Forbidden Structures for Planar Perfect Consecutively Colourable Graphs
Discussiones Mathematicae Graph Theory, 2017 A consecutive colouring of a graph is a proper edge colouring with posi- tive integers in which the colours of edges incident with each vertex form an interval of integers.
Borowiecka-Olszewska Marta +1 more
doaj +1 more source
Progress on perfect graphs [PDF]
Mathematical Programming, 2003 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Maria Chudnovsky +3 more
openaire +1 more source
Electronic Notes in Discrete Mathematics, 1999 Two graphs \(G\) and \(H\) on the vertex set \(V\) are \(P_4\)-isomorphic if there is a permutation \(\pi\) on \(V\) such that, for all subsets \(S\) of \(V\), \(S\) induces a chordless \(P_4\) in \(G\) if and only if \(\pi (S)\) induces a \(P_4\) in \(H\). The author characterizes all graphs \(P_4\)-isomorphic to a bipartite graph. For example, we can
openaire +1 more source