FLC OF C550 HAS RWY INCURSION DURING TAXI DUE TO ARPT CONSTRUCTION AND POOR TXWY SIGNAGE.

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WE HAD JUST LANDED ON RWY 25R AND TURNED OFF AT A6 THEN CALLED GND. GND ADVISED US TO 'TURN L AND HOLD SHORT OF RWY 19R. THERE WAS CONSTRUCTION ON RWY 19L AND TXWY B WHICH WE HAD TO PASS THROUGH; WHICH MEANT THAT ALL RWY; TAXI CTRLINE AND HOLD SHORT LINES ARE POOR OR NON EXISTENT. WE HELD SHORT OF RWY 19R IN A POS WE FELT APPROPRIATE TO MAKE OUR XING AND WAITED FOR CLRNC TO CROSS. FROM OUR POS IN THE COCKPIT AND OUR LOCATION ON THE TXWY IT WAS DIFFICULT TO SEE THE OPPOSITE SIDES OF RWY 19R DUE TO THE FACT THE RWY IS HIGH CTRED. GND CTL CALLED TO 'CROSS RWY 19R WITHOUT DELAY; ACFT HOLDING IN POS.' WE PWRED UP AND STARTED TO CROSS AND THEN REALIZED THAT WE WERE NOT IN A POS TO GO STRAIGHT ACROSS; WE FOUND OURSELVES PROCEEDING N ON RWY 19R. GND ASKED WHAT WE WERE DOING AND WE ADVISED WE WERE XING THE RWY. THEY THEN ADVISED US TO HOLD SHORT; TO WHICH WE RESPONDED THAT WE WERE ALREADY ON THE RWY. REALIZING WHAT HAD HAPPENED WE IMMEDIATELY HEADED FOR THE NEAREST TXWY; WHICH WAS AHEAD AND TO THE R. GND THEN TOLD US TO EXPEDITE TO TXWY W AND TURN L. SO WE PROCEEDED FURTHER DOWN THE RWY TO TXWY W AND TURNED L AS INSTRUCTED. WE FEEL THAT THIS WAS CAUSED BY POOR TXWY AND RWY MARKING IN A CONSTRUCTION AREA AND INCOMPLETE TAXI INSTRUCTION ON THE PART OF GND CTL. WITH THIS IN MIND; IT IS ADVISABLE THAT DURING CONSTRUCTION; TEMPORARY MARKINGS SHOULD BE CLR AND UPDATED PERIODICALLY. ALSO; GND SHOULD GIVE SPECIFIC INSTRUCTION AND ADVISORIES FOR TAXIING THROUGH THOSE AREAS. SUPPLEMENTAL INFO FROM ACN 389881: FROM MY UNDERSTANDING; WHEN AN AIRPLANE IS CLRED TO CROSS A RWY THAT RWY IS DEDICATED SOLELY TO 1 ACFT. ON THIS OCCASION IT SEEMS THAT THE TWR CTLRS AT LAS CLRED 2 OR 3 ACFT FOR THE SAME RWY AT ONE TIME. ALSO BETTER INSTRUCTIONS ON THE PART OF THE GND CTLR COULD HAVE ALLEVIATED THE SIT. PERHAPS 'TAXI ACROSS RWY 19R STRAIGHT AHEAD' OR SOMETHING TO THAT AFFECT. ALSO TO KEEP THIS FROM HAPPENING IN THE FUTURE; CONFIRMATION OF EXACT TAXI INSTRUCTIONS (BY THE PLT) FROM THE CTLR WILL HELP. I WOULD ALSO LIKE TO MENTION THAT WHEN WE LEFT LAS LATER IN THE DAY; WE NOTICED 2 ACFT DOING THE EXACT SAME THING THAT WE DID. THE REACTION FROM THE CTLR WAS TO ADVISE THE OTHER ACFT THAT NEXT TIME THEY MIGHT WANT TO TAXI STRAIGHT AHEAD FOR A MORE EXPEDITIOUS WAY TO CROSS THE RWY!