AbstractA lower bound is given for the number of hexagonal faces in a simple map on a closed surface whose graph is 3-connected depending on the numbers of i-gonal faces, i ≠ 6, and the genus of the surface
AbstractLet Rn be the root face valency of a random, rooted n-edged 3-polytope, Xn the valency of a ...
AbstractA combination of the refined finite lattice method and transfer matrices allows a radical in...
AbstractWe construct a polyhedral 2-manifold of genus 2 embedded in Euclidean 3-space, and hence ori...
AbstractA lower bound is given for the number of hexagonal faces in a simple map on a closed surface...
AbstractIf P is a simple 3-dimesional polytope and pi is the number of i sided faces of P then(p+t−1...
AbstractWe prove the inequality Σn≥7 (n−6) pn≤v−12 for any 3-dimensional polytope with v vertices an...
AbstractLet pk(P) denote the number of k-gonal faces of the 3-polytope P. Necessary and sufficient c...
AbstractThe smallest number of vertices, edges, or faces of any 3-polytope with no Hamiltonian path ...
AbstractTwo theorems of A. Kotzig are extended, as follows: 1.(1) A. Kotzig proved in 1963 that ever...
Klee in 1966 proved that every simple d-polyhedron P with v facets has at least v−d+1 vertices. Grün...
AbstractA set of n nonconcurrent lines in the projective plane (called an arrangment) divides the pl...
AbstractThe smallest number of vertices, edges, or faces of any 3-polytope with no Hamiltonian circu...
AbstractIt is shown that for every value of an integer k, k⩾11, there exist 3-valent 3-connected pla...
AbstractThis paper gives a proof of the fact that the chromatic number of an orientable surface of g...
AbstractAn Euler characteristic argument indicates that if K, a girth three graph, triangulates the ...
AbstractLet Rn be the root face valency of a random, rooted n-edged 3-polytope, Xn the valency of a ...
AbstractA combination of the refined finite lattice method and transfer matrices allows a radical in...
AbstractWe construct a polyhedral 2-manifold of genus 2 embedded in Euclidean 3-space, and hence ori...
AbstractA lower bound is given for the number of hexagonal faces in a simple map on a closed surface...
AbstractIf P is a simple 3-dimesional polytope and pi is the number of i sided faces of P then(p+t−1...
AbstractWe prove the inequality Σn≥7 (n−6) pn≤v−12 for any 3-dimensional polytope with v vertices an...
AbstractLet pk(P) denote the number of k-gonal faces of the 3-polytope P. Necessary and sufficient c...
AbstractThe smallest number of vertices, edges, or faces of any 3-polytope with no Hamiltonian path ...
AbstractTwo theorems of A. Kotzig are extended, as follows: 1.(1) A. Kotzig proved in 1963 that ever...
Klee in 1966 proved that every simple d-polyhedron P with v facets has at least v−d+1 vertices. Grün...
AbstractA set of n nonconcurrent lines in the projective plane (called an arrangment) divides the pl...
AbstractThe smallest number of vertices, edges, or faces of any 3-polytope with no Hamiltonian circu...
AbstractIt is shown that for every value of an integer k, k⩾11, there exist 3-valent 3-connected pla...
AbstractThis paper gives a proof of the fact that the chromatic number of an orientable surface of g...
AbstractAn Euler characteristic argument indicates that if K, a girth three graph, triangulates the ...
AbstractLet Rn be the root face valency of a random, rooted n-edged 3-polytope, Xn the valency of a ...
AbstractA combination of the refined finite lattice method and transfer matrices allows a radical in...
AbstractWe construct a polyhedral 2-manifold of genus 2 embedded in Euclidean 3-space, and hence ori...
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