AbstractThe dominating circuit conjecture states that every cyclically 4-edge-connected cubic graph has a dominating circuit. We show that this is equivalent to the statement that any two edges of such a cyclically 4-edge-connected graph are contained in a dominating circuit
AbstractFor a graph G, let σ̄k+3(G)=min{d(x1)+d(x2)+⋯+d(xk+3)−|N(x1)∩N(x2)∩⋯∩N(xk+3)|∣x1,x2,…,xk+3 a...
We prove that every cubic bridgeless graph $G$ contains a $2$-factor which intersects all (minimal) ...
AbstractIn this paper we characterize the class of trees, unicyclic graphs and cubic graphs for whic...
AbstractThe well-known dominating circuit conjecture has several interesting reformulations, for exa...
AbstractSnarks are cyclically 4-edge-connected cubic graphs with girth at least 5 and with no 3-edge...
An eulerian subgraph of a graph is called a circuit. As shown by Harary and Nash-Williams, the exist...
We show that the conjectures by Matthews and Sumner (every 4-connected claw-free graph is Hamiltonia...
AbstractWe show that the conjectures by Matthews and Sumner (every 4-connected claw-free graph is Ha...
AbstractLet G be a 2-connected graph on n vertices such that d(x) + d(y) + d(z) ⩾ n for all triples ...
We show that the conjectures by Matthews and Sumner (every 4-connected claw-free graph is hamiltonia...
AbstractA set S of vertices in a graph G is said to be an edge-dominating set if every edge in G is ...
Let G be a 2-connected graph on n vertices such that d(x) + d(y) + d(z) n for all triples of indepe...
AbstractThe first result states that every 4-connected graph G with minimum degree δ and connectivit...
Let T be a trail of a graph G. T is a spanning trail (S-trail) if T contains all vertices of G. T is...
Let $G$ be a graph. A total dominating set in a graph $G$ is a set $S$ of vertices of $G$ such that ...
AbstractFor a graph G, let σ̄k+3(G)=min{d(x1)+d(x2)+⋯+d(xk+3)−|N(x1)∩N(x2)∩⋯∩N(xk+3)|∣x1,x2,…,xk+3 a...
We prove that every cubic bridgeless graph $G$ contains a $2$-factor which intersects all (minimal) ...
AbstractIn this paper we characterize the class of trees, unicyclic graphs and cubic graphs for whic...
AbstractThe well-known dominating circuit conjecture has several interesting reformulations, for exa...
AbstractSnarks are cyclically 4-edge-connected cubic graphs with girth at least 5 and with no 3-edge...
An eulerian subgraph of a graph is called a circuit. As shown by Harary and Nash-Williams, the exist...
We show that the conjectures by Matthews and Sumner (every 4-connected claw-free graph is Hamiltonia...
AbstractWe show that the conjectures by Matthews and Sumner (every 4-connected claw-free graph is Ha...
AbstractLet G be a 2-connected graph on n vertices such that d(x) + d(y) + d(z) ⩾ n for all triples ...
We show that the conjectures by Matthews and Sumner (every 4-connected claw-free graph is hamiltonia...
AbstractA set S of vertices in a graph G is said to be an edge-dominating set if every edge in G is ...
Let G be a 2-connected graph on n vertices such that d(x) + d(y) + d(z) n for all triples of indepe...
AbstractThe first result states that every 4-connected graph G with minimum degree δ and connectivit...
Let T be a trail of a graph G. T is a spanning trail (S-trail) if T contains all vertices of G. T is...
Let $G$ be a graph. A total dominating set in a graph $G$ is a set $S$ of vertices of $G$ such that ...
AbstractFor a graph G, let σ̄k+3(G)=min{d(x1)+d(x2)+⋯+d(xk+3)−|N(x1)∩N(x2)∩⋯∩N(xk+3)|∣x1,x2,…,xk+3 a...
We prove that every cubic bridgeless graph $G$ contains a $2$-factor which intersects all (minimal) ...
AbstractIn this paper we characterize the class of trees, unicyclic graphs and cubic graphs for whic...
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