AbstractWe prove a conjecture of Saito that if a graph G with δ≥3 has no cycle of length 1 (mod 3), then G has an induced subgraph which is isomorphic to the Petersen graph. The above result strengthened the result by Dean et al. that every 2-connected graph with δ≥3 has a (1 mod 3)-cycle if G is not isomorphic to the Petersen graph
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...
Let G be a triangle-free graph with δ(G) ≥ 2 and σ4(G) ≥ |V(G)|+2. Let S ⊂ V(G) consist of less than...
AbstractS. Locke proved that the cycle space of a 3-connected nonhamiltonian graph with minimum degr...
AbstractWe prove a conjecture of Saito that if a graph G with δ≥3 has no cycle of length 1 (mod 3), ...
AbstractIt is proven that if G is a 3-cyclable graph on n vertices, with minimum degree δ and with a...
AbstractFan [G. Fan, Distribution of cycle lengths in graphs, J. Combin. Theory Ser. B 84 (2002) 187...
AbstractMoon and Moser in 1963 conjectured that if G is a 3-connected planar graph on n vertices, th...
AbstractDirac proved in 1952 that every 2-connected graph of order n and minimum degree k admits a c...
AbstractFor a graph G, define the parameters α(G)=max{|S| |S is an independent set of vertices of G}...
AbstractLet γ(G) denote the domination number of a graph G and let Cn□G denote the cartesian product...
AbstractWe prove the following two theorems.Let n, g⩾3 and let I⊆{3,…,g}. There exists an n-regular ...
AbstractWe show that for each ℓ⩾4 every sufficiently large oriented graph G with δ+(G),δ−(G)⩾⌊|G|/3⌋...
AbstractFor every graph G, let σ2(G)=min{d(x)+d(y):xy∉E(G)}. The main result of the paper says that ...
AbstractFor any natural number k, a graph G is said to be pancyclic modk if it contains a cycle of e...
AbstractWe show that for all positive ε, an integer N(ε) exists such that if G is any graph of order...
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...
Let G be a triangle-free graph with δ(G) ≥ 2 and σ4(G) ≥ |V(G)|+2. Let S ⊂ V(G) consist of less than...
AbstractS. Locke proved that the cycle space of a 3-connected nonhamiltonian graph with minimum degr...
AbstractWe prove a conjecture of Saito that if a graph G with δ≥3 has no cycle of length 1 (mod 3), ...
AbstractIt is proven that if G is a 3-cyclable graph on n vertices, with minimum degree δ and with a...
AbstractFan [G. Fan, Distribution of cycle lengths in graphs, J. Combin. Theory Ser. B 84 (2002) 187...
AbstractMoon and Moser in 1963 conjectured that if G is a 3-connected planar graph on n vertices, th...
AbstractDirac proved in 1952 that every 2-connected graph of order n and minimum degree k admits a c...
AbstractFor a graph G, define the parameters α(G)=max{|S| |S is an independent set of vertices of G}...
AbstractLet γ(G) denote the domination number of a graph G and let Cn□G denote the cartesian product...
AbstractWe prove the following two theorems.Let n, g⩾3 and let I⊆{3,…,g}. There exists an n-regular ...
AbstractWe show that for each ℓ⩾4 every sufficiently large oriented graph G with δ+(G),δ−(G)⩾⌊|G|/3⌋...
AbstractFor every graph G, let σ2(G)=min{d(x)+d(y):xy∉E(G)}. The main result of the paper says that ...
AbstractFor any natural number k, a graph G is said to be pancyclic modk if it contains a cycle of e...
AbstractWe show that for all positive ε, an integer N(ε) exists such that if G is any graph of order...
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...
Let G be a triangle-free graph with δ(G) ≥ 2 and σ4(G) ≥ |V(G)|+2. Let S ⊂ V(G) consist of less than...
AbstractS. Locke proved that the cycle space of a 3-connected nonhamiltonian graph with minimum degr...
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