AbstractA graph is said to be k-variegated if its vertex set can be partitioned into k equal parts such that each vertex is adjacent to exactly one vertex from every other part not containing it. Bednarek and Sanders [1] posed the problem of characterizing k-variegated graphs. V.N. Bhat-Nayak, S.A. Choudum and R.N. Naik [2] gave the characterization of 2-variegated graphs. In this paper we characterize k-variegated graphs for k ⩾ 3
The graph of a polytope is the graph whose vertex set is the set of vertices of the polytope, and wh...
Kn(m) is a regular n-partite graph with nm vertices. We prove that K12s+7(3α) and K12s+7(3α·2) can b...
AbstractBose and Laskar introduced the tetrahedral graph G, whose points may be identified with the ...
AbstractA graph is said to be k-variegated if its vertex set can be partitioned into k equal parts s...
A graph is said to be k-variegated if its vertex set can be partitioned into k equal parts such that...
AbstractTwo theorems of A. Kotzig are extended, as follows: 1.(1) A. Kotzig proved in 1963 that ever...
AbstractA graph is bivariegated if its vertex set can be partitioned into two equal sets such that e...
AbstractIn this paper we prove the following: let G be a graph with eG edges, which is (k − 1)-edge-...
AbstractWe prove the conjecture made by O. V. Borodin in 1976 that the vertex set of every planar gr...
AbstractWe prove that any non-planar 3-connected graph with at least 6 vertices contains a cycle wit...
AbstractIt is shown that the number of vertices of valency 2 in a critical graph with chromatic inde...
12 pagesInternational audienceWe describe ${\rm Forb}\{K_{1,3}, \overline {K_{1,3}}\}$, the class of...
An undirected simple graph G = (V,E) is called antimagic if there exists an injective function f: E ...
AbstractRecently J. Zaks formulated the following Eberhard-type problem:Let (p5, p6, …) be a finite ...
AbstractFor integers k, s with 0 ⩽ s ⩽ k, let G(n, k, s) be the class of graphs on n vertices not co...
The graph of a polytope is the graph whose vertex set is the set of vertices of the polytope, and wh...
Kn(m) is a regular n-partite graph with nm vertices. We prove that K12s+7(3α) and K12s+7(3α·2) can b...
AbstractBose and Laskar introduced the tetrahedral graph G, whose points may be identified with the ...
AbstractA graph is said to be k-variegated if its vertex set can be partitioned into k equal parts s...
A graph is said to be k-variegated if its vertex set can be partitioned into k equal parts such that...
AbstractTwo theorems of A. Kotzig are extended, as follows: 1.(1) A. Kotzig proved in 1963 that ever...
AbstractA graph is bivariegated if its vertex set can be partitioned into two equal sets such that e...
AbstractIn this paper we prove the following: let G be a graph with eG edges, which is (k − 1)-edge-...
AbstractWe prove the conjecture made by O. V. Borodin in 1976 that the vertex set of every planar gr...
AbstractWe prove that any non-planar 3-connected graph with at least 6 vertices contains a cycle wit...
AbstractIt is shown that the number of vertices of valency 2 in a critical graph with chromatic inde...
12 pagesInternational audienceWe describe ${\rm Forb}\{K_{1,3}, \overline {K_{1,3}}\}$, the class of...
An undirected simple graph G = (V,E) is called antimagic if there exists an injective function f: E ...
AbstractRecently J. Zaks formulated the following Eberhard-type problem:Let (p5, p6, …) be a finite ...
AbstractFor integers k, s with 0 ⩽ s ⩽ k, let G(n, k, s) be the class of graphs on n vertices not co...
The graph of a polytope is the graph whose vertex set is the set of vertices of the polytope, and wh...
Kn(m) is a regular n-partite graph with nm vertices. We prove that K12s+7(3α) and K12s+7(3α·2) can b...
AbstractBose and Laskar introduced the tetrahedral graph G, whose points may be identified with the ...
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