. . "RIV/00216208:11320/11:10101030" . . . . . . "215742" . . . . "http://dx.doi.org/10.1016/j.endm.2011.10.026" . . "[9E9E2A0B4E82]" . "New approach to Petersen coloring"@en . . . . "New approach to Petersen coloring" . "December" . "New approach to Petersen coloring"@en . "NL - Nizozemsko" . "1"^^ . "\u0160\u00E1mal, Robert" . "Petersen coloring (defined by Jaeger [On graphic-minimal spaces, Ann. Discrete Math. 8 (1980)]) is a mapping from the edges of a cubic graph to the edges of the Petersen graph, so that three edges adjacent at a vertex are mapped to three edges adjacent at a vertex. The existence of such mapping for every cubic bridgeless graph is known to imply the truth of the Cycle double cover conjecture and of the Berge-Fulkerson conjecture. We develop Jaeger\u02BCs alternate formulation of Petersen coloring in terms of special five-edge colorings. We suggest a weaker conjecture, and provide new techniques to solve it. On a related note, we provide a counterexample to a stronger conjecture by DeVos, Ne\u0161et\u0159il, and Raspaud [On edge-maps whose inverse preserves flows and tensions, Graph Theory in Paris, 2006] that asked for an oriented version of Petersen coloring. Keywords: Petersen coloring; nowhere-zero flows; cycle-double cover" . "1"^^ . "38" . "10.1016/j.endm.2011.10.026" . "New approach to Petersen coloring" . "Petersen coloring (defined by Jaeger [On graphic-minimal spaces, Ann. Discrete Math. 8 (1980)]) is a mapping from the edges of a cubic graph to the edges of the Petersen graph, so that three edges adjacent at a vertex are mapped to three edges adjacent at a vertex. The existence of such mapping for every cubic bridgeless graph is known to imply the truth of the Cycle double cover conjecture and of the Berge-Fulkerson conjecture. We develop Jaeger\u02BCs alternate formulation of Petersen coloring in terms of special five-edge colorings. We suggest a weaker conjecture, and provide new techniques to solve it. On a related note, we provide a counterexample to a stronger conjecture by DeVos, Ne\u0161et\u0159il, and Raspaud [On edge-maps whose inverse preserves flows and tensions, Graph Theory in Paris, 2006] that asked for an oriented version of Petersen coloring. Keywords: Petersen coloring; nowhere-zero flows; cycle-double cover"@en . . . "6"^^ . "coloring; Petersen; approach; New"@en . "11320" . "RIV/00216208:11320/11:10101030!RIV12-GA0-11320___" . "P(1M0545), P(GPP201/10/P337), Z(MSM0021620838)" . "000294972800004" . . "Electronic Notes in Discrete Mathematics" . . . . "1571-0653" .