Results 111 to 120 of about 8,623,913 (295)
On the number of cliques in graphs with a forbidden minor
Journal of Combinatorial Theory, Series B, 2017 Reed and Wood and independently Norine, Seymour, Thomas, and Wollan proved that for each positive integer $t$ there is a constant $c(t)$ such that every graph on $n$ vertices with no $K_t$-minor has at most $c(t)n$ cliques. Wood asked in 2007 if we can take $c(t) = c^t$ for some absolute constant $c$.
Jacob Fox, Fan Wei
openaire +4 more sources
A new graph construction of unbounded clique-width.
, 2016 We define permutation-partition graphs by replacing one part of a 2K2-free bipartite graph (a bipartite chain graph) by an induced linear forest. We show that this hereditary graph class is of of unbounded clique-width (with a new graph construction of ...
Korpelainen, Nicholas
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On Odd Covers of Cliques and Disjoint Unions
Journal of Graph Theory, EarlyView.ABSTRACT Babai and Frankl posed the “odd cover problem” of finding the minimum cardinality of a collection of complete bipartite graphs such that every edge of the complete graph of order n $n$ is covered an odd number of times. In a previous paper with O'Neill, some of the authors proved that this value is always ⌈ n / 2 ⌉ $\lceil n/2\rceil $ or ⌈ n /
Calum Buchanan +7 more
wiley +1 more source
Flexible List Coloring of Graphs With Maximum Average Degree Less Than 3
Journal of Graph Theory, EarlyView.ABSTRACT In the flexible list coloring problem, we consider a graph G $G$ and a color list assignment L $L$ on G $G$, as well as a subset U ⊆ V ( G ) $U\subseteq V(G)$ for which each u ∈ U $u\in U$ has a preferred color p ( u ) ∈ L ( u ) $p(u)\in L(u)$. Our goal is to find a proper L $L$‐coloring ϕ $\phi $ of G $G$ such that ϕ ( u ) = p ( u ) $\phi (u)=
Richard Bi, Peter Bradshaw
wiley +1 more source
Sparse Graphs With Local Covering Conditions on Edges
Journal of Graph Theory, EarlyView.ABSTRACT In 1988, Erdős suggested the question of minimizing the number of edges in a connected n $n$‐vertex graph where every edge is contained in a triangle. Shortly after, Catlin, Grossman, Hobbs, and Lai resolved this in a stronger form. In this paper, we study a natural generalization of the question of Erdős in which we replace “triangle” with ...
Debsoumya Chakraborti +3 more
wiley +1 more source
The clique number and some Hamiltonian properties of graphs [PDF]
Contributions to Mathematics, 2021 Rao Li
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Some results on the independence number of connected domination critical graphs
AKCE International Journal of Graphs and Combinatorics, 2018 A --critical graph is a graph with connected domination number and for any pair of non-adjacent vertices and of . Let and be respectively the clique number and the independence number of a graph.
P. Kaemawichanurat, T. Jiarasuksakun
doaj +1 more source
Bounds for graph energy in terms of vertex covering and clique numbers
Electronic Journal of Graph Theory and Applications, 2019 Let G be a simple graph with n vertices, m edges and having adjacency eigenvalues λ1, λ2, …, λn. The energy E(G) of the graph G is defined as E(G) = ∑i = 1n∣λi∣.
Hilal A. Ganie +3 more
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Path Degeneracy and Applications
Journal of Graph Theory, EarlyView.ABSTRACT In this work, we relate girth and path‐degeneracy in classes with sub‐exponential expansion, with explicit bounds for classes with polynomial expansion and proper minor‐closed classes that are tight up to a constant factor (and tight up to second order terms if a classical conjecture on existence of g $g$‐cages is verified). As an application,
Yuquan Lin, Patrice Ossona de Mendez
wiley +1 more source
A New Spectral Bound on the Clique Number of Graphs
, 2010 Many computer vision and patter recognition problems are intimately related to the maximum clique problem. Due to the intractability of this problem, besides the development of heuristics, a research direction consists in trying to find good bounds on ...
Pelillo M +5 more
core +1 more source