AbstractIn 1970, Dirac conjectured that for every integer k⩾4, there exists a vertex k-critical graph which contains no critical edge. In this paper, we construct an infinite family of (α,ω)-graphs. A direct consequence of this construction will be that Dirac's conjecture holds whenever k−1 is not prime
AbstractA set S of vertices in a graph G is a total dominating set of G if every vertex of G is adja...
A set S of vertices in a graph G is a total dominating set of G if every vertex of G is adjacent to ...
Let G be a graph on n 3 vertices. Dirac's minimum degree condition is the condition that all vertice...
AbstractIn 1970, Dirac conjectured that for every integer k⩾4, there exists a vertex k-critical grap...
AbstractThe conjecture of Dirac that every 4-critical planar graph has a vertex of degree at most 4 ...
AbstractWe prove that Kχ(G) is the only vertex critical graph G with χ(G)⩾Δ(G)⩾6 and ω(H(G))⩽⌊Δ(G)2⌋...
AbstractIn this paper, we give a generalization of a well-known result of Dirac that given any k ver...
A graph G is k-critical if it has chromatic number k, but every proper subgraph of G is (k − 1)–colo...
AbstractLet X be a subset of the vertex set of a graph G. We denote by κ(X) the smallest number of v...
In 1960, Dirac put forward the conjecture that r-connected 4-critical graphs exist for every r ≥ 3. ...
AbstractIt is thought that T. Gallai posed the following problem concerning a construction due to G....
AbstractThe vertex-critical graph conjecture (critical graph conjecture respectively) states that ev...
AbstractLet G be a graph on n ⩾ 3 vertices. Dirac's minimum degree condition is the condition that a...
Let $r$ be any positive integer. We prove that for every sufficiently large $k$ there exists a $k$-c...
AbstractLet G be a graph with K(G)=h. A vertex v of G is called k-critical if k(G−v)=h−1. Generalizi...
AbstractA set S of vertices in a graph G is a total dominating set of G if every vertex of G is adja...
A set S of vertices in a graph G is a total dominating set of G if every vertex of G is adjacent to ...
Let G be a graph on n 3 vertices. Dirac's minimum degree condition is the condition that all vertice...
AbstractIn 1970, Dirac conjectured that for every integer k⩾4, there exists a vertex k-critical grap...
AbstractThe conjecture of Dirac that every 4-critical planar graph has a vertex of degree at most 4 ...
AbstractWe prove that Kχ(G) is the only vertex critical graph G with χ(G)⩾Δ(G)⩾6 and ω(H(G))⩽⌊Δ(G)2⌋...
AbstractIn this paper, we give a generalization of a well-known result of Dirac that given any k ver...
A graph G is k-critical if it has chromatic number k, but every proper subgraph of G is (k − 1)–colo...
AbstractLet X be a subset of the vertex set of a graph G. We denote by κ(X) the smallest number of v...
In 1960, Dirac put forward the conjecture that r-connected 4-critical graphs exist for every r ≥ 3. ...
AbstractIt is thought that T. Gallai posed the following problem concerning a construction due to G....
AbstractThe vertex-critical graph conjecture (critical graph conjecture respectively) states that ev...
AbstractLet G be a graph on n ⩾ 3 vertices. Dirac's minimum degree condition is the condition that a...
Let $r$ be any positive integer. We prove that for every sufficiently large $k$ there exists a $k$-c...
AbstractLet G be a graph with K(G)=h. A vertex v of G is called k-critical if k(G−v)=h−1. Generalizi...
AbstractA set S of vertices in a graph G is a total dominating set of G if every vertex of G is adja...
A set S of vertices in a graph G is a total dominating set of G if every vertex of G is adjacent to ...
Let G be a graph on n 3 vertices. Dirac's minimum degree condition is the condition that all vertice...
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