Results 71 to 80 of about 69,865 (208)
Forbidden subgraphs and the Kőnig property
Electronic Notes in Discrete Mathematics, 2011 Abstract A graph has the Kőnig property if its matching number equals its transversal number. Lovasz proved a characterization of graphs having the Kőnig property by forbidden subgraphs, restricted to graphs with a perfect matching. Korach, Nguyen, and Peis proposed an extension of Lovaszʼs result to a characterization of all graphs having the Kőnig ...
Mitre Costa Dourado +4 more
openaire +1 more source
Theory and Applications of GraphsA class G of graphs is called hereditary if it is closed under taking induced subgraphs. We denote by G^{apex} the class of graphs G that contain a vertex v such that G − v is in G.
Jagdeep Singh +2 more
doaj +1 more source
Graph Classes Generated by Mycielskians
Discussiones Mathematicae Graph Theory, 2020 In this paper we use the classical notion of weak Mycielskian M′(G) of a graph G and the following sequence: M′0(G) = G, M′1(G) = M′(G), and M′n(G) = M′(M′n−1(G)), to show that if G is a complete graph of order p, then the above sequence is a generator ...
Borowiecki Mieczys law +3 more
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Signed Projective Cubes, a Homomorphism Point of View
Journal of Graph Theory, Volume 113, Issue 1, Page 38-56, September 2026.ABSTRACT The (signed) projective cubes, as a special class of graphs closely related to the hypercubes, are on the crossroad of geometry, algebra, discrete mathematics and linear algebra. Defined as Cayley graphs on binary groups, they represent basic linear dependencies.
Meirun Chen +2 more
wiley +1 more source
Forbidden induced subgraph of the Comparability Graph and Three Colored Posets
, 2018 The cover-incomparability graph of a poset P is the edge-union of the covering and the incomparability graph of P. As a continuation of the study of 3-colored diagrams we characterize some forbidden ⊲ - preserving subposets of the posets whose cover ...
Sibi C Babu, Baiju Sukumaran, Athul T B
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Forbidden Pairs and (k,m)-Pancyclicity
Discussiones Mathematicae Graph Theory, 2017 A graph G on n vertices is said to be (k, m)-pancyclic if every set of k vertices in G is contained in a cycle of length r for each r ∈ {m, m+1, . . . , n}.
Crane Charles Brian
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Fractional List Packing for Layered Graphs
Journal of Graph Theory, Volume 113, Issue 1, Page 19-37, September 2026.ABSTRACT The fractional list packing number χ ℓ • ( G ) of a graph G is a graph invariant that has recently arisen from the study of disjoint list‐colourings. It measures how large the lists of a list‐assignment L : V ( G ) → 2 N need to be to ensure the existence of a “perfectly balanced” probability distribution on proper L‐colourings, that is, such ...
Stijn Cambie, Wouter Cames van Batenburg
wiley +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
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Long Induced Paths in K s , s‐Free Graphs
Journal of Graph Theory, Volume 112, Issue 4, Page 438-441, August 2026.ABSTRACT More than 40 years ago, Galvin, Rival, and Sands showed that every K s , s‐free graph containing an n‐vertex path must contain an induced path of length f ( n ), where f ( n ) → ∞ as n → ∞. Recently, it was shown by Duron, Esperet, and Raymond that one can take f ( n ) = ( log log n ) 1 / 5 − o ( 1 ).
Zach Hunter +3 more
wiley +1 more source
Finding a heaviest vertex-weighted triangle is not harder than matrix multiplication [PDF]
, 2009 We show that a maximum-weight triangle in an undirected graph with n vertices and real weights assigned to vertices can be found in time O(n(omega) + n(2+o(1))), where omega is the exponent of the fastest matrix multiplication algorithm. By the currently
Lingas, Andrzej, +4 more
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