Results 1 to 10 of about 1,022,716 (217)
Domination Game Critical Graphs
Discussiones Mathematicae Graph Theory, 2015 The domination game is played on a graph G by two players who alternately take turns by choosing a vertex such that in each turn at least one previously undominated vertex is dominated. The game is over when each vertex becomes dominated.
Bujtás Csilla +2 more
doaj +4 more sources
On 3-flow-critical graphs [PDF]
European Journal of Combinatorics, 2021 A bridgeless graph $G$ is called $3$-flow-critical if it does not admit a nowhere-zero $3$-flow, but $G/e$ has for any $e\in E(G)$. Tutte's $3$-flow conjecture can be equivalently stated as that every $3$-flow-critical graph contains a vertex of degree three. In this paper, we study the structure and extreme edge density of $3$-flow-critical graphs. We
Jiaao Li +4 more
openalex +3 more sources
Multicolor star-critical Ramsey numbers and Ramsey-good graphs [PDF]
Electronic Journal of Graph Theory and Applications, 2022 This paper seeks to develop the multicolor version of star-critical Ramsey numbers, which serve as a measure of the strength of the corresponding Ramsey numbers. We offer several general theorems, some of which focus on Ramsey-good cases (i.e., cases in
Mark Rowland Budden, Elijah DeJonge
doaj +2 more sources
, 2010 This work introduces the concept of \emph{upper-critical graphs}, in a complementary way of the conventional (lower)critical graphs: an element $x$ of a graph $G$ is called \emph{critical} if $ (G-x)
Jose Antonio Martin H
openalex +3 more sources
The Maximal Length of 2-Path in Random Critical Graphs [PDF]
Journal of Applied Mathematics, 2018 Given a graph, its 2-core is the maximal subgraph of G without vertices of degree 1. A 2-path in a connected graph is a simple path in its 2-core such that all vertices in the path have degree 2, except the endpoints which have degree ⩾3.
Vonjy Rasendrahasina +2 more
doaj +2 more sources
Counting Critical Subgraphs in k-Critical Graphs [PDF]
Combinatorica, 2021 Update the concluding remarks, due to counterexamples to some problems asked in the earlier ...
Ma, Jie, Yang, Tianchi
openaire +3 more sources
k-Critical Graphs in $$P_5$$-Free Graphs [PDF]
Theoretical Computer Science, 2020 Given two graphs $H_1$ and $H_2$, a graph $G$ is $(H_1,H_2)$-free if it contains no induced subgraph isomorphic to $H_1$ or $H_2$. Let $P_t$ be the path on $t$ vertices. A graph $G$ is $k$-vertex-critical if $G$ has chromatic number $k$ but every proper induced subgraph of $G$ has chromatic number less than $k$.
Cameron, Kathie +3 more
openaire +5 more sources
On b-vertex and b-edge critical graphs [PDF]
Opuscula Mathematica, 2015 A \(b\)-coloring is a coloring of the vertices of a graph such that each color class contains a vertex that has a neighbor in all other color classes, and the \(b\)-chromatic number \(b(G)\) of a graph \(G\) is the largest integer \(k\) such that \(G ...
Noureddine Ikhlef Eschouf +1 more
doaj +1 more source
Critically n-Connected Graphs [PDF]
Proceedings of the American Mathematical Society, 1972 The following result is proved. Every n-connected graph contains either a vertex whose removal results in a graph which is also n-connected or a vertex of degree less than (3n 1)/2. Introduction. A graph G is said to be n-connected if the removal of fewer than n vertices from G neither disconnects it nor reduces it to the trivial graph consisting of a ...
Chartrand, G., Kaugars, A., Lick, D. R.
openaire +1 more source
Packing chromatic vertex-critical graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 The packing chromatic number $\chi_{\rho}(G)$ of a graph $G$ is the smallest integer $k$ such that the vertex set of $G$ can be partitioned into sets $V_i$, $i\in [k]$, where vertices in $V_i$ are pairwise at distance at least $i+1$.
Sandi Klavžar, Douglas F. Rall
doaj +1 more source