Results 81 to 90 of about 8,970,965 (255)
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
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
Clique coloring of binomial random graphs [PDF]
, 2018 A clique colouring of a graph is a colouring of the vertices so that no maximal clique is monochromatic (ignoring isolated vertices). The smallest number of colours in such a colouring is the clique chromatic number.
Prałat, Paweł +5 more
core +1 more source
Line Graphs of Multigraphs and the Forbidden Graph E 6
Journal of Graph Theory, EarlyView.ABSTRACT The line graph Γ of a multigraph Δ is the graph whose vertices are the edges of Δ, where two such edges are adjacent if and only if they meet in a single vertex of Δ. We provide several characterizations of such line graphs and in particular show that a graph is a line graph if and only if it does not contain one of the 32 graphs, all of which
Hans Cuypers
wiley +1 more source
On maximizing clique, clique-Helly and hereditary clique-Helly induced subgraphs [PDF]
, 2019 Clique-Helly and hereditary clique-Helly graphs are polynomial-time recognizable. Recently, we presented a proof that the clique graph recognition problem is NP-complete [L. Alcón, L. Faria, C.M.H. de Figueiredo, M. Gutierrez, Clique graph recognition is
Faria, L. +3 more
core
Clique with given number of outer-incident edges
, 2019 We prove that finding a clique with a given number of outer-incident edges in a given graph is difficult.
Thinh D. Nguyen (6385907)
core +1 more source
A Note on Extendable Sets of Colorings and Rooted Minors
Journal of Graph Theory, EarlyView.ABSTRACT DeVos and Seymour proved that for every set C $C$ of 3‐colorings of a set X $X$ of vertices, there exists a plane graph G $G$ with vertices of X $X$ incident with the outer face such that a 3‐coloring of X $X$ extends to a 3‐coloring of G $G$ if and only if it belongs to C $C$.
Zdeněk Dvořák, Jan M. Swart
wiley +1 more source
, 1972 An algorithm for finding a maximum clique in an arbitrary graph is described. The algorithm has a worst-case time bound of $k(1.286)^{n}$ for some constant $k$, where $n$ is the number of vertices in the graph.
Tarjan, Robert Endre
core +5 more sources
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
doaj +1 more source